If $\sin 2\theta = \cos \theta ,\,\,0 < \theta < \pi $, then the possible values of $\theta $ are
${90^o},{60^o},{30^o}$
${90^o},{150^o},{60^o}$
${90^o},{45^o},{150^o}$
${90^o},{30^o},{150^o}$
The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta = 2,$ is
The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is
The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
$cos (\alpha \,-\,\beta ) = 1$ and $cos (\alpha +\beta ) = 1/e$ , where $\alpha , \beta \in [-\pi , \pi ]$ . Number of pairs of $(\alpha ,\beta )$ which satisfy both the equations is