General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$
$\theta = \frac{{n\pi }}{7} + \frac{\pi }{{14}}$
$\theta = \frac{{n\pi }}{7} + \frac{\pi }{5}$
$\theta = \frac{{n\pi }}{7} + \frac{\pi }{2}$
$\theta = \frac{{n\pi }}{7} + \frac{\pi }{3}$
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
The equation $\sin x + \sin y + \sin z = - 3$ for $0 \le x \le 2\pi ,$ $0 \le y \le 2\pi ,$ $0 \le z \le 2\pi $, has
The value of $\theta $ in between ${0^o}$ and ${360^o}$ and satisfying the equation $\tan \theta + \frac{1}{{\sqrt 3 }} = 0$ is equal to
Number of roots of the equation ${\cos ^2}x + \frac{{\sqrt 3 + 1}}{2}\sin x - \frac{{\sqrt 3 }}{4} - 1 = 0$ which lie in the interval $[-\pi,\pi ]$ is
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal