The correct option is C 5 2π sin ^ 1 ( sinθ nbsp; nbsp;) nbsp; =θ π nbsp;/ 2 ≤θ≤π nbsp;/ 2 Hence, first we write the expression such t ...

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Integration of Trigonometric Functions

sin-1sin5=

Question

$s i n^{- 1} (s i n 5) =$

5

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5 - 2 π

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2 π - 5

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2 π + 5

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Solution

The correct option is C $5 - 2 π$
${sin}^{- 1} (sin θ) = θ - \frac{π}{2} \leq θ \leq \frac{π}{2}$
Hence, first we write the expression such that $- \frac{π}{2} \leq θ \leq \frac{π}{2}$
${sin}^{- 1} (sin 5) = {sin}^{- 1} sin (5 - 2 π)$ (Since $5 - 2 π > - π / 2$ )
$s i n^{- 1} s i n 5 = 5 - 2 π$

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