$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $
${45^o}$ and ${60^o}$
${45^o}$ and ${90^o}$
${45^o}$only
${90^o}$only
If $\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$ is the solution of $4 \cos \theta+5 \sin \theta=1$, then the value of $\tan \alpha$ is
The smallest positive values of $x$ and $y$ which satisfy $\tan (x - y) = 1,\,$ $\sec (x + y) = \frac{2}{{\sqrt 3 }}$ are
The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$
The smallest positive root of the equation $tanx\, -\, x = 0$ lies on