Let $f(x) =x^2$ and $g(x)=\sin x$ for all $x\in R$ .Then the set of all $x$ satisfying $(fogogof)(x)=(gogof)(x)$ where $fog(x)=f(g(x))$ is

Question

$\begin{array}{1 1}(a)\;\pm \sqrt{n\pi};n\in \{0,1,2\}\\(b)\;\pm\sqrt{ n\pi};n \in \{1,2\}\\(c)\;\large\frac{\pi}{2}+\normalsize 2n\pi;n\in \{...-2,-1,0,1,2\}\\(d)\;2n\pi;n\in \{...-2,-1,0,1,2...\}\end{array}$