If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $
$n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{3}$
$n\pi \pm \frac{\pi }{4}$
$n\pi \pm \frac{\pi }{2}$
If $2(\sin x - \cos 2x) - \sin 2x(1 + 2\sin x)2\cos x = 0$ then
The number of solutions of the equation $\cos \left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^{2} 2 x, x \in[-3 \pi$ $3 \pi]$ is
The equation $3\cos x + 4\sin x = 6$ has
For which value of $x$ ; $cosx > sinx,$ where $x\, \in \,\,\left( {\frac{\pi }{2}\,,\,\frac{{3\pi }}{2}} \right)$
If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are