If $1 + \cot \theta = {\rm{cosec}}\theta $, then the general value of $\theta $ is
$n\pi + \frac{\pi }{2}$
$2n\pi - \frac{\pi }{2}$
$2n\pi + \frac{\pi }{2}$
None of these
Let $A=\left\{\theta \in R \mid \cos ^2(\sin \theta)+\sin ^2(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\}$. Then, $A \cap B$
Solve $2 \cos ^{2} x+3 \sin x=0$
If $\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 ,$ then
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :