If $\frac{{1 - \cos 2\theta }}{{1 + \cos 2\theta }} = 3$, then the general value of $\theta $ is
$2n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{6}$
$2n\pi \pm \frac{\pi }{3}$
$n\pi \pm \frac{\pi }{3}$
If sum of all the solutions of the equation $8\cos x \cdot \left( {\cos \left( {\frac{\pi }{6} + x} \right) \cdot \cos \left( {\frac{\pi }{6} - x} \right) - \frac{1}{2}} \right) = 1$ in $\left[ {0,\pi } \right]$ is $k\pi $then $k$ is equal to :
If $sin^4\,\,\alpha + 4\,cos^4\,\,\beta + 2 = 4\sqrt 2\,\,sin\,\alpha \,cos\,\beta ;$ $\alpha \,,\,\beta \, \in \,[0,\pi ],$ then $cos( \alpha + \beta)$ is equal to
The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is
The sum of solutions of the equation $\frac{\cos \mathrm{x}}{1+\sin \mathrm{x}}=|\tan 2 \mathrm{x}|, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4},-\frac{\pi}{4}\right\}$ is :
The number of solutions to $\sin x=\frac{6}{x}$ with $0 \leq x \leq 12 \pi$ is