The number of values of $x$ for which $sin\,\, 2x + cos\,\, 4x = 2$ is
$0$
$1$
$2$
infinite
If $\sqrt 3 \tan 2\theta + \sqrt 3 \tan 3\theta + \tan 2\theta \tan 3\theta = 1$, then the general value of $\theta $ is
If both roots of quadratic equation ${x^2} + \left( {\sin \,\theta + \cos \,\theta } \right)x + \frac{3}{8} = 0$ are positive and distinct then complete set of values of $\theta $ in $\left[ {0,2\pi } \right]$ is
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$
If $\cos p\theta = \cos q\theta ,p \ne q$, then
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 :