The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is
$1$
$2$
$3$
$4$
Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$
If $sin^2x + sinx \,cosx -6cos^2x = 0$ and $-\frac{\pi}{2} < x < 0$, then the value of $cos2x$, is
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
If the solution for $\theta $ of $\cos p\theta + \cos q\theta = 0,\;p > 0,\;q > 0$ are in $A.P.$, then the numerically smallest common difference of $A.P.$ is
The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi + x}}{3}} \right) = 1$ is