If $\theta $ and $\phi $ are acute satisfying $\sin \theta = \frac{1}{2},$ $\cos \phi = \frac{1}{3},$ then $\theta + \phi \in $
$\left( {\frac{\pi }{3},\,\frac{\pi }{2}} \right)$
$\left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)$
$\left( {\frac{{2\pi }}{3},\,\frac{{5\pi }}{6}} \right)$
$\left( {\frac{{5\pi }}{6},\pi } \right)$
If $\sin x=\frac{3}{5}, \cos y=-\frac{12}{13},$ where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.
Find the general solution of the equation $\sec ^{2} 2 x=1-\tan 2 x$
The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are
The solution set of $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ in the interval $[0,\,\,2\pi ]$ is
The sum of solutions in $x \in (0,2\pi )$ of the equation, $4\cos (x).\cos \left( {\frac{\pi }{3} - x} \right).\cos \left( {\frac{\pi }{3} + x} \right) = 1$ is equal to