Let $S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}$
$\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}$ Then.
$S =\left\{\frac{\pi}{12}\right\}$
$S =\left\{\frac{2 \pi}{3}\right\}$
$\sum_{\theta \in S} \theta=\frac{\pi}{2}$
$\sum_{\theta \in S} \theta=\frac{3 \pi}{4}$
Solve $\sin 2 x-\sin 4 x+\sin 6 x=0$
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
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-
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is