The equation $\sin x + \sin y + \sin z = - 3$ for $0 \le x \le 2\pi ,$ $0 \le y \le 2\pi ,$ $0 \le z \le 2\pi $, has
One solution
Two sets of solutions
Four sets of solutions
No solution
If $5\cos 2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0, - \pi < \theta < \pi $, then $\theta = $
$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to
The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if
The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to
The sum of solutions in $x \in (0,2\pi )$ of the equation, $4\cos (x).\cos \left( {\frac{\pi }{3} - x} \right).\cos \left( {\frac{\pi }{3} + x} \right) = 1$ is equal to