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 all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is

The number of solutions of $tan\, (5\pi\, cos\, \theta ) = cot (5 \pi \,sin\, \theta )$ for $\theta$ in $(0, 2\pi )$ is :

$2{\sin ^2}x + {\sin ^2}2x = 2,\, – \pi < x < \pi ,$ then $x = $

$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r – 1}}}}{{\cos \,{2^r}}}} $ is equal to