The general solution of $\frac{{\tan \,2x\, - \,\tan \,x}}{{1\, + \,\tan \,x\,\tan \,2x}}\, = \,1$ is
$\phi $
$n\pi \pm \frac{\pi }{3}$
$n\pi + \frac{\pi }{4}$
$n\pi + \frac{\pi }{6}\left( {n \in z} \right)$
The number of solutions of the equation $\sin (9 x)+\sin (3 x)=0$ in the closed interval $[0,2 \pi]$ is
The number of real solutions of the equation $2 \sin 3 x+\sin 7 x-3=0$, which lie in the interval $[-2 \pi, 2 \pi]$ is
If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the value of $\theta $ and $\phi $ are
Let $A=\left\{\theta \in R:\left(\frac{1}{3} \sin \theta+\frac{2}{3} \cos \theta\right)^2=\frac{1}{3} \sin ^2 \theta+\frac{2}{3} \cos ^2 \theta\right\}$.Then
The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is