Let `f(x)=x^2a n dg(x)=sinxfora l lx in Rdot` Then the set of all `x` satisfying `(fogogof)(x)=(gogof)(x),w h e r e(fog)(x)=f(g(x)),` is (a) `+-sqrt(npi),n in {0,1,2, dot}` (b)`+-sqrt(npi),n in {1,2, dot}` (c) `pi/2+2npi,n in { ,-2,-1,0,1,2}` (d) `2npi,n in { ,-2,-1,0,1,2, }`

Explanation

To solve the problem, we need to find the set of all \( x \) satisfying the equation \( (f \circ g \circ g \circ f)(x) = (g \circ g \circ f)(x) \), where \( f(x) = x^2 \) and \( g(x) = \sin x \).

### Step 1: Define the compositions
First, we need to compute \( f(g(x)) \) and \( g(f(x)) \).

- \( g(x) = \sin x \)
- \( f(g(x)) = f(\sin x) = (\sin x)^2 \)

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