If the sum of solutions of the system of equations $2 \sin ^{2} \theta-\cos 2 \theta=0$ and $2 \cos ^{2} \theta+3 \sin \theta=0$ in the interval $[0,2 \pi]$ is $k \pi$, then $k$ is equal to.
$3$
$6$
$9$
$12$
Find the general solution of the equation $\sin x+\sin 3 x+\sin 5 x=0$
If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta + \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta = $
If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is