General solution of the equation $\cot \theta - \tan \theta = 2$ is
$n\pi + \frac{\pi }{4}$
$\frac{{n\pi }}{2} + \frac{\pi }{8}$
$\frac{{n\pi }}{2} \pm \frac{\pi }{8}$
None of these
The number of pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin (x + y)$ and $|x| + |y| = 1$ is
If $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ the number of solutions of the given equation when $x \in\left[0, \frac{\pi}{2}\right]$ is
The equation ${\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0$ is solvable for
$sin 3\theta = 4 sin\, \theta \,sin \,2\theta \,sin \,4\theta$ in $0\, \le \,\theta\, \le \, \pi$ has :
The sum of all values of $x$ in $[0,2 \pi]$, for which $\sin x+\sin 2 x+\sin 3 x+\sin 4 x=0$, is equal to: