If $(2\cos x - 1)(3 + 2\cos x) = 0,\,0 \le x \le 2\pi $, then $x = $
$\frac{\pi }{3}$
$\frac{\pi }{3},\frac{{5\pi }}{3}$
$\frac{\pi }{2},\frac{{5\pi }}{3},{\cos ^{ - 1}}\left( { - \frac{3}{2}} \right)$
$\frac{{5\pi }}{3}$
The number of solutions $x$ of the equation $\sin \left(x+x^2\right)-\sin \left(x^2\right)=\sin x$ in the interval $[2,3]$ is
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true
The number of pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin (x + y)$ and $|x| + |y| = 1$ is
The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta - 20\sin 2\theta = 20p + 35$ , will have a solution is
If $\sin x=\frac{3}{5}, \cos y=-\frac{12}{13},$ where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.