If $5\cos 2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0, - \pi < \theta < \pi $, then $\theta = $
$\frac{\pi }{3}$
$\frac{\pi }{3},{\cos ^{ - 1}}\frac{3}{5}$
${\cos ^{ - 1}}\frac{3}{5}$
$\frac{\pi }{3},\pi - {\cos ^{ - 1}}\frac{3}{5}$
$\tan \,{20^o}\cot \,{10^o}\cot \,{50^o}$ is equal to
The value of $\theta $ in between ${0^o}$ and ${360^o}$ and satisfying the equation $\tan \theta + \frac{1}{{\sqrt 3 }} = 0$ is equal to
The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
If $\sin 2\theta = \cos 3\theta $ and $\theta $ is an acute angle, then $\sin \theta $ is equal to
The number of real solutions $x$ of the equation $\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$ is