iCON Education - Trigonometric Ratios & Identities AP-EAPCET Test

Candidate Name

Student

Exam Name

AP-EAPCET

Test Name

Trigonometric Ratios & Identities

Subject

Mathematics

← Back to Trigonometric Ratios & Identities

Remaining Time

01:30:00

Question 1: Palette 1/90

AP-EAPCET 2025 MCQ

$ \sin \frac{\pi}{12} \sin \frac{2 \pi}{12} \sin \frac{3 \pi}{12} \sin \frac{4 \pi}{12} \sin \frac{5 \pi}{12} \sin \frac{6 \pi}{12}= $

$\frac{\sqrt{3}}{16 \sqrt{2}}$

$\frac{\sqrt{3}}{8 \sqrt{2}}$

$\frac{1}{32}$

$\frac{1}{16}$

Question 2: Palette 2/90

AP-EAPCET 2025 MCQ

If $A+B+C+D=2 \pi$, then $\sin A+\sin B+\sin C+\sin D=$

$4 \sin \left(\frac{A+B}{4}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A+C}{4}\right) \cos \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{2}\right) \sin \left(\frac{A+D}{2}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$

Question 3: Palette 3/90

AP-EAPCET 2025 MCQ

If $\cos x+\sin x=\frac{1}{2}$ and $0

$\frac{1+\sqrt{7}}{4}$

$\frac{1-\sqrt{7}}{4}$

$\frac{4-\sqrt{7}}{3}$

$-\frac{(4+\sqrt{7})}{3}$

Question 4: Palette 4/90

AP-EAPCET 2025 MCQ

If $\sin \theta+2 \cos \theta=1$ and $\theta$ belongs to 4 th quadrant (not lying on the coordinate axes), then $7 \cos \theta+6 \sin \theta=$

$\frac{4}{17}$

$\frac{7}{17}$

$\frac{4}{5}$

Question 5: Palette 5/90

AP-EAPCET 2025 MCQ

If $A$ and $B$ are acute angles satisfying $3 \cos ^2 A+2 \cos ^2 B=4$ and $\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A}$, then $A+2 B=$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

Question 6: Palette 6/90

AP-EAPCET 2025 MCQ

$ \begin{aligned} & \left(4 \cos ^2 \frac{\pi}{20}-1\right)\left(4 \cos ^2 \frac{3 \pi}{20}-1\right) \\ & \left(4 \cos ^2 \frac{5 \pi}{20}+1\right)\left(4 \cos ^2 \frac{7 \pi}{20}-1\right)\left(4 \cos ^2 \frac{9 \pi}{20}-1\right)= \end{aligned} $

$1 / 2$

Question 7: Palette 7/90

AP-EAPCET 2025 MCQ

If $A$ and $B$ are the values such that $(A+B)$ and $(A-B)$ are not odd multiples of $\frac{\pi}{2}$ and $2 \tan (A+B)=3 \tan (A-B)$, then $\sin A \cos A=$

$\sin B \cos B$

$5 \sin B \cos B$

$\sin 2 B$

$\cos 2 B$

Question 8: Palette 8/90

AP-EAPCET 2025 MCQ

If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=k$, then $\frac{4 k}{3}=$

$\sin \left(\frac{4 \pi}{3}\right)$

$\cos \left(\frac{2 \pi}{3}\right)$

$\tan \left(\frac{\pi}{3}\right)$

$\sec \left(\frac{2 \pi}{3}\right)$

Question 9: Palette 9/90

AP-EAPCET 2025 MCQ

$ \cos 13^{\circ} \sin 17^{\circ} \sin 21^{\circ} \cos 47^{\circ}= $

$\frac{1}{32}(1+\sqrt{2}-\sqrt{3})$

$\frac{1}{16}(1+\sqrt{3}+\sqrt{5})$

$\frac{1}{16}(2+\sqrt{3}-\sqrt{5})$

$\frac{1}{32}(1+2 \sqrt{3}-\sqrt{5})$

Question 10: Palette 10/90

AP-EAPCET 2025 MCQ

$ \sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}= $

$\sqrt{5}$

$\frac{1}{4}(\sqrt{5}+1)(\sqrt{10+2 \sqrt{5}})$

$\frac{1}{4}(\sqrt{5}-1)(\sqrt{10+2 \sqrt{5}})$

Question 11: Palette 11/90

AP-EAPCET 2025 MCQ

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=$

$4 \sqrt{3}$

$-4 \sqrt{3}$

Question 12: Palette 12/90

AP-EAPCET 2025 MCQ

If $\cos \theta=\frac{-3}{5}$ and $\theta$ does not lie in second quadrant, then $\tan \frac{\theta}{2}=$

-2

-1

Question 13: Palette 13/90

AP-EAPCET 2025 MCQ

If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos ^2 \frac{x}{4}+\sin \frac{x}{4}, x \in R$, then $\alpha-\beta=$

$\frac{1}{4}$

$\frac{9}{4}$

Question 14: Palette 14/90

AP-EAPCET 2025 MCQ

If $A$ and $B$ are positive acute angles satisfying $3 \cos ^2 A+2 \cos ^2 B=4$ and $\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A}$, then $A+2 B=$

$30^{\circ}$

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

Question 15: Palette 15/90

AP-EAPCET 2025 MCQ

If $\sin x-\sin y=\frac{27}{65}$ and $\cos x-\cos y=\frac{-21}{65}$, then $\sin (x+y)=$

$-\frac{63}{65}$

$\frac{16}{65}$

$\frac{63}{65}$

$-\frac{16}{65}$

Question 16: Palette 16/90

AP-EAPCET 2025 MCQ

If $\alpha, \beta$ are the acute angles such that $\frac{\sin \alpha}{\sin \beta}=\frac{6}{5}$ and $\frac{\cos \alpha}{\cos \beta}=\frac{9}{5 \sqrt{5}}$, then $\sin \alpha=$

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{2}{3}$

Question 17: Palette 17/90

AP-EAPCET 2025 MCQ

If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$, then $a: b=$

$4: 1$

$8: 1$

$3: 2$

$2: 1$

Question 18: Palette 18/90

AP-EAPCET 2025 MCQ

An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms . A person on the ground observed that the angle of elevation of the plane is changed from $15^{\circ}$ to $30^{\circ}$ in the duration of 50 seconds, then the speed of the plane (in kmph ) is

100

720

360

540

Question 19: Palette 19/90

AP-EAPCET 2025 MCQ

If $A+B=\frac{\pi}{4}$, then $\frac{\cos B-\sin B}{\cos B+\sin B}=$

$\sin A$

$\cos A$

$\tan A$

$\cot A$

Question 20: Palette 20/90

AP-EAPCET 2025 MCQ

If $7 \cos \theta-\sin \theta=5$ and $\tan \theta>0$, then $\tan \theta=$

$\frac{7}{12}$

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{12}{7}$

Question 21: Palette 21/90

AP-EAPCET 2025 MCQ

$ \sin ^3 10^{\circ}+\sin ^3 50^{\circ}-\sin ^3 70^{\circ}= $

$\frac{-3}{8}$

$\frac{3}{4}$

$\frac{\sqrt{3}}{2}$

$\frac{-1}{3}$

Question 22: Palette 22/90

AP-EAPCET 2025 MCQ

$ \begin{aligned} \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\circ} \sin 4^{\circ}} & +\frac{1}{\sin 89^{\circ} \sin 90^{\circ}}= \end{aligned} $

$\frac{\sin 1^{\circ}}{\tan 1^{\circ}}$

$\frac{1}{\sin ^2 \varphi}$

$\frac{\cot 1^{\circ}}{\sin 1^{\circ}}$

$\frac{\tan 1^{\circ}}{\cos 1^{\circ}}$

Question 23: Palette 23/90

AP-EAPCET 2025 MCQ

$ \cos ^3 \frac{\pi}{8} \cos \frac{3 \pi}{8}+\sin ^3 \frac{\pi}{8} \sin \frac{3 \pi}{8}= $

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{1}{4}$

Question 24: Palette 24/90

AP-EAPCET 2025 MCQ

If $A+B+C=\frac{\pi}{4}$, then $\sin 4 A+\sin 4 B+\sin 4 C=$

$4 \cos 2 A \cos 2 B \cos 2 C$

$4 \sin 2 A \sin 2 B \sin 2 C$

$1+4 \sin 2 A \sin 2 B \sin 2 C$

$1+4 \cos 2 A \cos 2 B \cos 2 C$

Question 25: Palette 25/90

AP-EAPCET 2025 MCQ

If $630^{\circ}<\theta<810^{\circ}$ and $\tan \theta=-\frac{7}{24}$, then $\cos \left(\frac{\theta}{4}\right)=$

$-\sqrt{\frac{7+5 \sqrt{2}}{10 \sqrt{2}}}$

$\sqrt{\frac{7+5 \sqrt{2}}{2 \sqrt{2}}}$

$-\sqrt{\frac{5 \sqrt{2}-7}{10 \sqrt{2}}}$

$\sqrt{\frac{5 \sqrt{2}-7}{2 \sqrt{2}}}$

Question 26: Palette 26/90

AP-EAPCET 2025 MCQ

For $\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ if $2 \cos \theta+\sin \theta=1$ and $7 \cos \theta+6 \sin \theta=k$, then the possible values of $k$ are

8,-2

6,2

12,4

7,6

Question 27: Palette 27/90

AP-EAPCET 2025 MCQ

$ \sum\limits_{k=0}^{12} \frac{1}{\sin \left((k+1) \frac{\pi}{6}+\frac{\pi}{4}\right) \sin \left(\frac{k \pi}{6}+\frac{\pi}{4}\right)}= $

$2(\sqrt{3}+1)$

$2(3-\sqrt{3})$

$2(2-\sqrt{3})$

$2(\sqrt{3}-1)$

Question 28: Palette 28/90

AP-EAPCET 2025 MCQ

If $\cos \alpha=\sec h \beta$, then $\beta=$

$\log (\sec \alpha+\tan \alpha)$

$\log (\sec \alpha-\tan \alpha)$

$\log (\sin \alpha+\cos \alpha)$

$\log (\cos \alpha+\cot \alpha)$

Question 29: Palette 29/90

AP-EAPCET 2024 MCQ

$ \tan ^2 \frac{\pi}{16}+\tan ^2 \frac{2 \pi}{16}+\tan ^2 \frac{3 \pi}{16}+\tan ^2 \frac{4 \pi}{16} $

$+\tan ^2 \frac{5 \pi}{16}+\tan ^2 \frac{6 \pi}{16}+\tan ^2 \frac{7 \pi}{16}$ is equal to

Question 30: Palette 30/90

AP-EAPCET 2024 MCQ

$ \begin{aligned} & \sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ} \\ & +\sin ^2 90^{\circ}+\sin ^2 96^{\circ}+\sin ^2 102^{\circ}+\sin ^2 138^{\circ}+\sin ^2 162^{\circ} \text { is } \\ & \text { equal to } \end{aligned} $

$\frac{11}{2}$

$\frac{9}{2}$

Question 31: Palette 31/90

AP-EAPCET 2024 MCQ

If $A B$ and $C$ are the angles of a triangle, then $\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1}$ is equal to

$-2 \tan \frac{B}{2}$

$-2 \cot \frac{B}{2}$

$2 \tan \frac{B}{2}$

$2 \cot \frac{B}{2}$

Question 32: Palette 32/90

AP-EAPCET 2024 MCQ

If $\cos \alpha+4 \cos \beta+9 \cos \gamma=0$ and $\sin \alpha+4 \sin \beta+9 \sin \gamma=0$, then 81 $\cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)$ is equal to

$1+8 \cos (\beta-\alpha)$

$\cos (\beta-\alpha)$

$1-36 \cos (\beta-\alpha)$

$1+6 \cos (\beta-\alpha)$

Question 33: Palette 33/90

AP-EAPCET 2024 MCQ

$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to

$\sin \alpha$

$\cos \alpha$

$\tan \alpha$

$\cot \alpha$

Question 34: Palette 34/90

AP-EAPCET 2024 MCQ

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

Question 35: Palette 35/90

AP-EAPCET 2024 MCQ

$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to

$-\frac{1}{8}$

$-\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{4}$

Question 36: Palette 36/90

AP-EAPCET 2024 MCQ

If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to

$\frac{21}{2}$

$\frac{25}{2}$

$\frac{23+5 \sqrt{21}}{2}$

$\frac{32+5 \sqrt{23}}{2}$

Question 37: Palette 37/90

AP-EAPCET 2024 MCQ

If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

$\frac{65}{2}$

$\frac{1}{32}$

$\frac{8}{3}$

Question 38: Palette 38/90

AP-EAPCET 2024 MCQ

$ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}= $

$-\frac{1}{8}$

$\frac{1}{32}$

$-\frac{1}{32}$

$\frac{1}{8}$

Question 39: Palette 39/90

AP-EAPCET 2024 MCQ

If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =

Question 40: Palette 40/90

AP-EAPCET 2024 MCQ

If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$

$4 \cos A \cos B \sin C$

$4 \cos A \sin B \cos C$

$4 \cos A \sin B \cos C-1$

$4 \sin A \cos B \sin C$

Question 41: Palette 41/90

AP-EAPCET 2024 MCQ

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$

Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$

$ =\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} $

Which of the following is correct ?

Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of (A)

Both $(A)$ and $(R)$ are true and $(R)$ is not correct explanationot (A)

(A) is true, ( $R$ ) is false

(A) is false, (R) is true.

Question 42: Palette 42/90

AP-EAPCET 2024 MCQ

If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$

$\frac{3 \times \sqrt{10}}{25}$

$\frac{3}{\sqrt{10}}$

$\frac{3}{25 \sqrt{10}}$

$\frac{\sqrt{10}}{3 \times 25}$

Question 43: Palette 43/90

AP-EAPCET 2024 MCQ

If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$

$\frac{1}{2}$

-1

$\frac{1}{\sqrt{2}}$

$-\frac{1}{\sqrt{2}}$

Question 44: Palette 44/90

AP-EAPCET 2024 MCQ

If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$

$\frac{\beta^2-\alpha^2}{\beta^2+\alpha^2}$

$\frac{2 \beta \alpha}{\beta^2-\alpha^2}$

$\frac{\beta^2+\alpha^2}{2 \beta \alpha}$

$\frac{2 a \beta}{\beta^2+\alpha^2}$

Question 45: Palette 45/90

AP-EAPCET 2024 MCQ

If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$

$4 \cos \frac{P}{2} \cos \frac{Q}{2}, \cos \frac{R}{2}-\cos \frac{\pi}{8}$

$4 \cos \frac{P}{2} \cos \frac{Q}{2} \cdot \sin \frac{R}{2}+\cos \frac{\pi}{8}$

$4 \sin \frac{P}{2} \cos \frac{Q}{2}, \sin \frac{R}{2}-\cos \frac{\pi}{8}$

Question 46: Palette 46/90

AP-EAPCET 2024 MCQ

If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$

$\frac{k}{k^2+1}$

$\frac{k^2+1}{k^2+2}$

$\frac{\sqrt{k^2-1}}{k}$

$\frac{\sqrt{k^2-1}}{\sqrt{k^2+1}}$

Question 47: Palette 47/90

AP-EAPCET 2024 MCQ

If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is

1st quadrant

2nd quadrant

3rd quadrant

4th quadrant

Question 48: Palette 48/90

AP-EAPCET 2024 MCQ

If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

$\frac{18}{5}$

$\frac{8}{5}$

$-\frac{8}{5}$

$-\frac{18}{5}$

Question 49: Palette 49/90

AP-EAPCET 2024 MCQ

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

Question 50: Palette 50/90

AP-EAPCET 2024 MCQ

If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$

$\frac{3}{4}$

$\frac{9}{16}$

$\frac{9}{8}$

Question 51: Palette 51/90

AP-EAPCET 2024 MCQ

$ \text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}= $

$\tan 35^{\circ}$

$\tan 55^{\circ}$

$\tan 20^{\circ}$

$\tan 70^{\circ}$

Question 52: Palette 52/90

AP-EAPCET 2024 MCQ

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=$

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

Question 53: Palette 53/90

AP-EAPCET 2024 MCQ

The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between

-2 and 5

-1 and 8

-3 and 6

-4 and 10

Question 54: Palette 54/90

AP-EAPCET 2024 MCQ

Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$

Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$

Which one of the following is correct?

Both (S1) and (S2) are true.

Both ( S 1 ) and ( S 2 ) are false.

(S1) is true, (S2) is false.

(S1) is false, (S2) is true.

Question 55: Palette 55/90

AP-EAPCET 2024 MCQ

$ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $

Question 56: Palette 56/90

AP-EAPCET 2024 MCQ

The maximum value of $12\sin x - 5\cos x + 3$ is

Question 57: Palette 57/90

AP-EAPCET 2024 MCQ

$\sin^2 16^\circ - \sin^2 76^\circ = $

$\frac{1}{2}$

$\frac{3}{4}$

Question 58: Palette 58/90

AP-EAPCET 2024 MCQ

By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is

1.07

0.965

1.035

0.93

Question 59: Palette 59/90

AP-EAPCET 2022 MCQ

If $\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta$, then the least $n$ for which $a_{2 n}=0$ is

Question 60: Palette 60/90

AP-EAPCET 2022 MCQ

If $\sin \theta=-\frac{3}{4}$, then $\sin 2 \theta=$

$\frac{3 \sqrt{7}}{8}$

$-\frac{3 \sqrt{7}}{8}$

$\frac{2 \sqrt{3}}{7}$

$-\frac{2 \sqrt{3}}{7}$

Question 61: Palette 61/90

AP-EAPCET 2022 MCQ

$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$

$\frac{\cos 1^{\circ}}{\sin 1^{\circ}}$

$\frac{\cos 1^{\circ}}{\sin ^2 1^{\circ}}$

$\frac{\sin 1^{\circ}}{\cos 1^{\circ}}$

$\frac{\sin ^2 1^{\circ}}{\cos 1^{\circ}}$

Question 62: Palette 62/90

AP-EAPCET 2022 MCQ

Which of the following trigonometric values are negative?

I. $\sin \left(-292^{\circ}\right)$

II. $\tan \left(-190^{\circ}\right)$

III. $\cos \left(-207^{\circ}\right)$

IV. $\cot \left(-222^{\circ}\right)$

II, III and IV

Only III

I and III

II and III

Question 63: Palette 63/90

AP-EAPCET 2022 MCQ

$\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=$

1/2

1/3

Question 64: Palette 64/90

AP-EAPCET 2022 MCQ

A true statement among the following identities is

$\sin 5 \theta=16 \cos ^4 \theta \sin \theta-12 \cos ^2 \theta \sin \theta+\sin \theta$

$\sin 5 \theta=16 \cos ^4 \theta-12 \cos ^2 \theta+1$

$\sin 5 \theta=16 \cos ^4 \theta \sin \theta+12 \cos ^2 \theta \sin \theta-\sin \theta$

$\sin 5 \theta=16 \cos ^4 \theta \sin \theta+12 \cos ^2 \theta \sin \theta+\sin \theta$

Question 65: Palette 65/90

AP-EAPCET 2022 MCQ

If $A+B+C=\pi, \cos B=\cos A \cos C$, then $\tan A \tan C=$

$\frac{1}{2}$

Question 66: Palette 66/90

AP-EAPCET 2022 MCQ

The value of $\tan \left(\frac{7 \pi}{8}\right)$ is

$\sqrt{2}-1$

$1-\sqrt{2}$

$1+\sqrt{2}$

$\frac{1}{1+\sqrt{2}}$

Question 67: Palette 67/90

AP-EAPCET 2022 MCQ

$1+\sec ^2 x \sin ^2 x=$

$\sin 2 x$

$\sin ^2 x$

$\tan ^2 x$

$\sec ^2 x$

Question 68: Palette 68/90

AP-EAPCET 2022 MCQ

If the identity $\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c$ holds for some $a, b, c \in Q$ then $(a, b, c)=$

$\left(\frac{1}{8}, \frac{3}{8}, \frac{1}{2}\right)$

$\left(\frac{1}{8}, \frac{1}{2}, \frac{3}{8}\right)$

$\left(\frac{1}{2}, \frac{1}{8}, \frac{3}{8}\right)$

$\left(\frac{1}{2}, \frac{3}{8}, \frac{1}{8}\right)$

Question 69: Palette 69/90

AP-EAPCET 2022 MCQ

The value of $\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$ is

$\cos 2 \theta$

$\cot 2 \theta$

$\tan 2 \theta$

$\operatorname{cosec} \theta+\sin \theta$

Question 70: Palette 70/90

AP-EAPCET 2022 MCQ

If $(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$ then $n=$

Question 71: Palette 71/90

AP-EAPCET 2022 MCQ

$\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=$

$\cos \theta-\sin \theta$

$\sin \theta-\cos \theta$

$\cos \theta+\sin \theta$

$(1-\tan \theta) \sin \theta$

Question 72: Palette 72/90

AP-EAPCET 2022 MCQ

If $\operatorname{cosech} x=\frac{4}{5}$, then $\sinh x=$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{2}{3}$

$\frac{2}{5}$

Question 73: Palette 73/90

AP-EAPCET 2021 MCQ

Let $\theta$ be an angle in the standard position such that the point $(-5,12)$ lies on its terminal side, then

$|\sin \theta|=-\sin \theta$

$|\cos \theta|=\cos \theta$

$|\tan \theta|=-\tan \theta$

$|\operatorname{cosec} \theta|=-\operatorname{cosec} \theta$

Question 74: Palette 74/90

AP-EAPCET 2021 MCQ

If $\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32}=2^m \operatorname{cosec} \frac{\pi}{n}$, then $m+n$ is equal to

Question 75: Palette 75/90

AP-EAPCET 2021 MCQ

If $A+B+C=\frac{3 \pi}{2}$, then $\cos 2 A+\cos 2 B+\cos 2 C$ is equal to

$1-4 \sin A \sin B \sin C$

$1+4 \sin A \sin B \sin C$

$1-2 \sin A \sin B \sin C$

$1+2 \sin A \sin B \sin C$

Question 76: Palette 76/90

AP-EAPCET 2021 MCQ

$\sinh (x+y) \cosh (x-y)$ is equal to

$\frac{1}{2}(\sinh 2 x+\sinh 2 y)$

$(\sinh 2 x+\sinh 2 y)$

$\frac{1}{2}(\sinh 2 x-\sinh 2 y)$

$(\sinh 2 x-\sinh 2 y)$

Question 77: Palette 77/90

AP-EAPCET 2021 MCQ

What is the value of $\cos \left(22 \frac{1}{2}\right)^{\circ}$ ?

$\sqrt{\frac{\sqrt{2}-1}{2 \sqrt{2}}}$

$\sqrt{\frac{\sqrt{2}+1}{2 \sqrt{2}}}$

$\sqrt{2}-1$

$\sqrt{2}+1$

Question 78: Palette 78/90

AP-EAPCET 2021 MCQ

If $\cos \theta=-\sqrt{\frac{3}{2}}$ and $\sin \alpha=\frac{-3}{5}$, where '$\theta$' does not lie in the third quadrant, then the value of $\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}$ is equal to

$\frac{7}{22}$

$\frac{5}{22}$

$\frac{9}{22}$

$\frac{22}{5}$

Question 79: Palette 79/90

AP-EAPCET 2021 MCQ

If $\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$, then $\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}$ is equal to

$\sin 2 \beta$

$\cos 2 \beta$

$\tan 2 \beta$

$\sec 2 \beta$

Question 80: Palette 80/90

AP-EAPCET 2021 MCQ

The sides of a triangle inscribed in a given circle subtend angles $\alpha, \beta, \gamma$ at the center. The minimum value of the AM of $\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$ and $\cos \left(\gamma+\frac{\pi}{2}\right)$ is equal to

$\frac{\sqrt{3}}{2}$

$\frac{-\sqrt{3}}{2}$

$\frac{-2}{\sqrt{3}}$

$\sqrt{2}$

Question 81: Palette 81/90

AP-EAPCET 2021 MCQ

In a $\triangle A B C$, if $3 \sin A+4 \cos B=6$ and $4 \sin B+3 \cos A=1$, then $\sin (A+B)$ is equal to

$1$

$\frac{1}{2}$

$0$

$\cos C$

Question 82: Palette 82/90

AP-EAPCET 2021 MCQ

$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to

$\tan 16 \alpha$

$0$

$\cot \alpha$

$\tan \alpha$

Question 83: Palette 83/90

AP-EAPCET 2021 MCQ

If $f(x)=\frac{\cot x}{1+\cot x}$ and $\alpha+\beta=\frac{5 \pi}{4}$, then the value of $f(\alpha) f(\beta)$ is equal to

$\frac{3}{2}$

$\frac{-3}{2}$

$\frac{-1}{2}$

$\frac{1}{2}$

Question 84: Palette 84/90

AP-EAPCET 2021 MCQ

In $\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$, then $\tan \frac{C}{8}$ is equal to

$\sqrt{6}+\sqrt{3}+\sqrt{2}-2$

$\sqrt{6}-\sqrt{3}-\sqrt{2}+2$

$\sqrt{6}-\sqrt{3}+\sqrt{2}-2$

$\sqrt{6}+\sqrt{3}-\sqrt{2}+2$

Question 85: Palette 85/90

AP-EAPCET 2021 MCQ

Mean of the values $\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$ is

$\frac{5}{9}$

$\frac{2}{3}$

$\frac{7}{9}$

$\frac{1}{9}$

Question 86: Palette 86/90

AP-EAPCET 2021 MCQ

When the coordinate axes are rotated through an angle 135$\Upsilon$, the coordinates of a point $P$ in the new system are known to be $(4,-3)$. Then find the coordinates of $P$ in the original system.

$\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$

$\left(\frac{-1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$

$\left(\frac{1}{\sqrt{2}}, \frac{-7}{\sqrt{2}}\right)$

$\left(\frac{-1}{\sqrt{2}}, \frac{-7}{\sqrt{2}}\right)$

Question 87: Palette 87/90

AP-EAPCET 2021 MCQ

The maximum value of $f(x)=\sin (x)$ in the interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$ is

$-$1

$\sqrt2$

Question 88: Palette 88/90

AP-EAPCET 2021 MCQ

$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)$ is equal to

$\tan 3 \alpha$

$\tan ^2 2 \alpha-\tan ^2 60 \gamma$

Question 89: Palette 89/90

AP-EAPCET 2021 MCQ

If $\sin \alpha - \cos \alpha = m$ and $\sin 2\alpha = n - {m^2}$, where $ - \sqrt 2 \le m \le \sqrt 2 $, then n is equal to

$-$2

Question 90: Palette 90/90

AP-EAPCET 2021 MCQ

If $\sinh u=\tan \theta$, then $\cosh u$ is equal to

$-\sec \theta$

$\sec \theta$

$\sin \theta$

$\cot \theta$

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