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 $n$ is any integer, then the general solution of the equation $\cos x - \sin x = \frac{1}{{\sqrt 2 }}$ is
If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right), \quad$ is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ is equal to:
The solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is
The sides of a triangle are $\sin \alpha ,\,\cos \alpha $ and $\sqrt {1 + \sin \alpha \cos \alpha } $ for some $0 < \alpha < \frac{\pi }{2}$. Then the greatest angle of the triangle is.....$^o$
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is