Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is

Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -

If $\sin \theta + \cos \theta = 1$ then the general value of $\theta $ is

If $1 + \sin x + {\sin ^2}x + .....$ to $\infty = 4 + 2\sqrt 3 ,\,0 < x < \pi ,$ then

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 real roots of the equation $cos^7x\,  +\,  sin^4x\,  =\,  1$  in the interval $(-\pi, \pi)$ are