If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
$(2n + 1)\frac{\pi }{4}$
$\frac{4}{{(2n + 1)\pi }}$
$4\pi (2n + 1)$
None of these
The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is
If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is
The roots of the equation $1 - \cos \theta = \sin \theta .\sin \frac{\theta }{2}$ is
The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is