If S = {x ∈ R : sin^-1 (x+1/√x^2+2x+2) - sin^-1 (x/√x^2+1) = π/4}, then

Question

If

\(S=\left\{x∈\mathbb{R}:sin^{-1}\left(\frac{x+1}{\sqrt{x^2+2x+2}}\right)-sin^{-1}\left(\frac{x}{\sqrt{x^2+1}}\right)=\frac{\pi}{4}\right\},\)

then

\(\displaystyle\sum_{x∈R}^{} \) \(\left(sin((x^2+x+5)\frac{\pi}{2})-cos((x^2+x+5)\pi)\right)\) is equal to ____.

Answer 1

Correct answer is 4

After solving this equation, we get