The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta = 2,$ is
$\frac{\pi }{3}$
$\frac{{5\pi }}{3}$
$\frac{{2\pi }}{3}$
$\frac{{4\pi }}{3}$
Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -
The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are
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
Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ 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