The sum of all values of $x$ in $[0,2 \pi]$, for which $\sin x+\sin 2 x+\sin 3 x+\sin 4 x=0$, is equal to:
$11 \pi$
$12 \pi$
$8 \pi$
$9 \pi$
If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ is-
Solve $\sin 2 x-\sin 4 x+\sin 6 x=0$
General solution of the equation $\cot \theta - \tan \theta = 2$ is
The number of solution of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0,2\pi )$ is
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal