The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are
$\frac{\pi }{9},\frac{\pi }{4}$
$\frac{\pi }{3},\frac{\pi }{9}$
$\frac{\pi }{6},\frac{\pi }{9}$
$\frac{\pi }{3},\frac{\pi }{4}$
$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to
Find the general solution of $\cos ec\, x=-2$
General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$
The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is
Let $S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^2 x}+9^{\tan ^2 x}=10\right\}$ and $\beta=\sum_{x \in S} \tan ^2\left(\frac{x}{3}\right)$, then $\frac{1}{6}(\beta-14)^2$ is equal to