Number of solutions of $\sqrt {\tan \theta }  = 2\sin \theta ,\theta  \in \left[ {0,2\pi } \right]$ is equal to 

Let $f(x) = \cos \sqrt {x,} $ then which of the following is true

If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to

If $sin^4\,\,\alpha + 4\,cos^4\,\,\beta + 2 = 4\sqrt 2\,\,sin\,\alpha \,cos\,\beta ;$ $\alpha \,,\,\beta \, \in \,[0,\pi ],$ then $cos( \alpha + \beta)$ is equal to

If $|k|\, = 5$ and ${0^o} \le \theta \le {360^o}$, then the number of different solutions of $3\cos \theta + 4\sin \theta = k$ is

The number of pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin (x + y)$ and $|x| + |y| = 1$ is