If $5\cos 2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0, - \pi < \theta < \pi $, then $\theta = $
$\frac{\pi }{3}$
$\frac{\pi }{3},{\cos ^{ - 1}}\frac{3}{5}$
${\cos ^{ - 1}}\frac{3}{5}$
$\frac{\pi }{3},\pi - {\cos ^{ - 1}}\frac{3}{5}$
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is
The positive integer value of $n>3$ satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)}$ is
Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.