Trigonometric Equations
158 Questions
1980
JEE Advanced
MCQ
IIT-JEE 1980
Given $A = {\sin ^2}\theta + {\cos ^4}\theta $ then for all real values of $\theta $
A.
$1 \le A \le 2$
B.
${3 \over 4} \le A \le 1$
C.
${13\over 16} \le A \le 1$
D.
${3 \over 4} \le A \le {{13} \over {16}}$
1980
JEE Advanced
Numerical
IIT-JEE 1980
Given $A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}$ and
$f\left( x \right) = \cos x - x\left( {1 + x} \right);$ find $f\left( A \right).$
$f\left( x \right) = \cos x - x\left( {1 + x} \right);$ find $f\left( A \right).$
Correct Answer: $$\left[ {{1 \over 2} - {\pi \over 3}\left( {1 + {\pi \over 3}} \right),\,{{\sqrt 3 } \over 2} - {\pi \over 6}\left( {1 + {\pi \over 6}} \right)} \right]$$
1980
JEE Advanced
Numerical
IIT-JEE 1980
Given $\alpha + \beta - \gamma = \pi ,$ prove that
$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$
$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$
Correct Answer: Solve it.
1980
JEE Advanced
Numerical
IIT-JEE 1980
For all $\theta $ in $\left[ {0,\,\pi /2} \right]$ show that, $\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).$
Correct Answer: Solve it.
1979
JEE Advanced
MCQ
IIT-JEE 1979
If $\alpha + \beta + \gamma = 2\pi ,$ then
A.
$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$
B.
$\tan {\alpha \over 2}\tan {\beta \over 2} + \tan {\beta \over 2}\tan {\gamma \over 2} + \tan {\gamma \over 2}\tan {\alpha \over 2} = 1$
C.
$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = - \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$
D.
None of these.
1979
JEE Advanced
MCQ
IIT-JEE 1979
If $\tan \theta = - {4 \over 3},then\sin \theta \,is\,$
A.
$ - {4 \over 5}\,but\,not\,{4 \over 5}$
B.
$ - {4 \over 5}\,or\,{4 \over 5}$
C.
${4 \over 5}\,\,but\,not\, - {4 \over 5}$
D.
None of these.
1979
JEE Advanced
Numerical
IIT-JEE 1979
(a) Draw the graph of $y = {1 \over {\sqrt 2 }}\left( {cinx + \cos x} \right)$ from $x = - {\pi \over 2}$ to $x = {\pi \over 2}$.
(b) If $\cos \left( {\alpha + \beta } \right) = {4 \over 5},\,\,\sin \,\left( {\alpha - \beta } \right) = \,{5 \over {13}},$ and $\alpha ,\,\beta $ lies between 0 and ${\pi \over 4}$, find tan2$\alpha $.
Correct Answer: $${56 \over {33}}$$
1978
JEE Advanced
Numerical
IIT-JEE 1978
If $\tan \alpha = {m \over {m + 1}}\,$ and $\tan \beta = {2 \over {2m + 1}},$ find the possible values of $\left( {\alpha + \beta } \right).$
Correct Answer: $$n\pi + {\pi \over 4}$$