If $0\, \le \,x\, < \frac{\pi }{2},$ then the number of values of $x$ for which $sin\,x -sin\,2x + sin\,3x=0,$ is

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.

Statement $-1:$ The number of common solutions of the trigonometric 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 two.

Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta  - 3\,sin\,\theta  = 0$ in the interval $[0, \pi ]$ is two.

The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to

If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is

Let $A=\left\{\theta \in R \mid \cos ^2(\sin \theta)+\sin ^2(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\}$. Then, $A \cap B$