If $a=sin^{-1}(sin\ 5)$ and $b=cos^{-1}(cos\ 5)$, then $a^2+b^2=$

Question

If the domain of the function $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha)\cup[\beta,\gamma]\cup[\delta,\infty)$, then $\alpha+\beta+\gamma+\delta$ is equal to

Answer 1

The result is $8\pi^2-40\pi+50$.

If \(a=sin^{-1}(sin\ 5)\) and \(b=cos^{-1}(cos\ 5)\), then \(a^2+b^2=\)

Solution and Explanation

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