If $\sin 2x + \sin 4x = 2\sin 3x,$ then $x =$
$\frac{{n\pi }}{3}$
$n\pi + \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{3}$
None of these
If $\sin x=\frac{3}{5}, \cos y=-\frac{12}{13},$ where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
Minimum value of the function $f(x) = \left| {\sin \,x + \cos \,x + \tan \,x + \cot \,x + \sec \,x + \ cosec\ x} \right|$ is equal to
The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.
If the equation $2\ {\sin ^2}x + \frac{{\sin 2x}}{2} = k$ , has atleast one real solution, then the sum of all integral values of $k$ is