The general value of $\theta $satisfying the equation $2{\sin ^2}\theta - 3\sin \theta - 2 = 0$ is
$n\pi + {( - 1)^n}\frac{\pi }{6}$
$n\pi + {( - 1)^n}\frac{\pi }{2}$
$n\pi + {( - 1)^n}\frac{{5\pi }}{6}$
$n\pi + {( - 1)^n}\frac{{7\pi }}{6}$
If $\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 ,$ then
Let,$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\}$. Then $n ( S )+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to.
Find the general solution of the equation $\sin 2 x+\cos x=0$
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
The solution of $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ is