$\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
The number of solutions to the equation $\cos ^4 x+\frac{1}{\cos ^2 x}=\sin ^4 x+\frac{1}{\sin ^2 x}$ in the interval $[0,2 \pi]$ is
The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is
If $\cos {40^o} = x$ and $\cos \theta = 1 - 2{x^2}$, then the possible values of $\theta $ lying between ${0^o}$ and ${360^o}$is
If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $
Find the general solution of the equation $\sin 2 x+\cos x=0$