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 $\cot (\alpha + \beta ) = 0,$ then $\sin (\alpha + 2\beta ) = $
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -
Number of solutions of $8cosx$ = $x$ will be
If$\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, where $0 < \theta < {180^o}$, then $\theta =$