The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is
$2$
$7$
$5$
$4$
If $a = \sin \frac{\pi }{{18}}\sin \frac{{5\pi }}{{18}}\sin \frac{{7\pi }}{{18}}$ and $x$ is the solution of the equatioin $y = 2\left[ x \right] + 2$ and $y = 3\left[ {x - 2} \right] ,$ where $\left[ x \right]$ denotes the integral part of $x,$ then $a$ is equal to :-
Solve $\sin 2 x-\sin 4 x+\sin 6 x=0$
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
If $2{\tan ^2}\theta = {\sec ^2}\theta ,$ then the general value of $\theta $ is
If $\sec 4\theta - \sec 2\theta = 2$, then the general value of $\theta $ is