Number of solution $(s)$ of the equation ${\cos ^2}2x + {\cos ^2}\frac{{5x}}{4} = \cos 2x\,{\cos ^2}5x$ in $\left[ {0,\frac{\pi }{3}} \right]$ is
$0$
$1$
$2$
$3$
Find the principal and general solutions of the question $\tan x=\sqrt{3}$.
If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in
Solve $\cos x=\frac{1}{2}$
Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are
$cos (\alpha \,-\,\beta ) = 1$ and $cos (\alpha +\beta ) = 1/e$ , where $\alpha , \beta \in [-\pi , \pi ]$ . Number of pairs of $(\alpha ,\beta )$ which satisfy both the equations is