The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is
$\frac{\pi}{6}$
$\frac{5 \pi}{6}$
$\pi$
$2 \pi$
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x - 7\sin x + 2 = 0$ is
If $1 + \cot \theta = {\rm{cosec}}\theta $, then the general value of $\theta $ is
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true
If $2(\sin x - \cos 2x) - \sin 2x(1 + 2\sin x)2\cos x = 0$ then