If $\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,$ then $\theta = $
$n\pi + \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
$n\pi - \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{6}$
Common roots of the equations $2{\sin ^2}x + {\sin ^2}2x = 2$ and $\sin 2x + \cos 2x = \tan x,$ are
If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then
The equation $\sin x + \cos x = 2$has
The general value $\theta $ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is
If $\tan \theta = - \frac{1}{{\sqrt 3 }}$ and $\sin \theta = \frac{1}{2}$, $\cos \theta = - \frac{{\sqrt 3 }}{2}$, then the principal value of $\theta $ will be