The general solution of $\frac{{\tan \,2x\, - \,\tan \,x}}{{1\, + \,\tan \,x\,\tan \,2x}}\, = \,1$ is
$\phi $
$n\pi \pm \frac{\pi }{3}$
$n\pi + \frac{\pi }{4}$
$n\pi + \frac{\pi }{6}\left( {n \in z} \right)$
Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ is equal to
The number of all possible values of $\theta$, where $0<\theta<\pi$, for which the system of equations
$ (y+z) \cos 3 \theta=(x y z) \sin 3 \theta $
$ x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} $
$ (x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta$ have a solution $\left(\mathrm{x}_0, \mathrm{y}_0, \mathrm{z}_0\right)$ with $\mathrm{y}_0 \mathrm{z}_0 \neq 0$, is
The number of values of $x$ for which $sin2x + sin4x = 2$ is
If $12{\cot ^2}\theta - 31\,{\rm{cosec }}\theta + {\rm{32}} = {\rm{0}}$, then the value of $\sin \theta $ is
The equation $5x^2+12x + 13 = 0$ and $ax^2+bx + c = 0$ have a common root, where $a,b,c$ are the sides of $\Delta ABC$,then find $\angle C$ ? .....$^o$