Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -
$0$
$1$
$2$
$5$
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is
The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is
The solution of the equation ${\cos ^2}x - 2\cos x = $ $4\sin x - \sin 2x,$ $\,(0 \le x \le \pi )$ is
The solution set of the system of equation
$x\,\, + \,\,y\,\, = \,\,\frac{{2\pi }}{3},\,{\rm{cos}}\,{\rm{x + }}\,{\rm{ cos}}\,{\rm{y}}\,{\rm{ = }}\,\frac{3}{2},$ where $x$ and $y$ are real in