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
$\frac{\pi}{6}$
$\frac{5 \pi}{6}$
$\pi$
$2 \pi$
The only value of $x$ for which ${2^{\sin x}} + {2^{\cos x}} > {2^{1 - (1/\sqrt 2 )}}$ holds, is
Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$ is
(where $sgn(.)$ denotes signum function) -
The set of values of $x$ for which the expression $\frac{{\tan 3x - \tan 2x}}{{1 + \tan 3x\tan 2x}} = 1$, is
Number of solutions of $5$ $cos^2 \theta -3 sin^2 \theta + 6 sin \theta cos \theta = 7$ in the interval $[0, 2 \pi] $ is :-
$\alpha=\sin 36^{\circ}$ is a root of which of the following equation