Let S be the set of all $$\alpha $$ $$ \in $$ R such that the equation, cos2x + $$\alpha $$sinx = 2$$\alpha $$– 7 has a solution. Then S is equal to :

The number of solutions of the equation
1 + sin⁴ x = cos²3x, $$x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]$$ is :

Let S = {$$\theta $$ $$ \in $$ [–2$$\pi $$, 2$$\pi $$] : 2cos²$$\theta $$ + 3sin$$\theta $$ = 0}. Then the sum of the elements of S is

The sum of all values of $$\theta $$ $$ \in $$$$\left( {0,{\pi \over 2}} \right)$$ satisfying
sin² 2$$\theta $$ + cos⁴ 2$$\theta $$ = $${3 \over 4}$$ is -