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Inverse Trigonometric Functions question

2023 · 13 Apr · Shift 1 · Q41

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JEE Main
Mathematics
Inverse Trigonometric Functions
2023 · 13 Apr · Shift 1 · Q41

Inverse Trigonometric Functions question

2023 · 13 Apr · Shift 1 · Q41

JEE MainMathematicsInverse Trigonometric FunctionsNumerical+4 / −1

If

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

, then

\sum_{x \in s}\left(\sin \left(\left(x^{2}+x+5\right) \frac{\pi}{2}\right)-\cos \left(\left(x^{2}+x+5\right) \pi\right)\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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