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Composition of Inverse Trigonometric Functions and Trigonometric Functions

sin - 1 sin 4...

Question

${sin}^{- 1} (sin 4) - {cos}^{- 1} (cos 5) =$

1

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π - 1

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1 - π

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- 1

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Solution

The correct option is C $1 - π$
${sin}^{- 1} (sin 4) - {cos}^{- 1} cos 5$
$\Rightarrow π - 4 - (2 π - 5)$
$\Rightarrow π - 4 - 2 π + 5$
$\Rightarrow - π + 1$
$\Rightarrow 1 - π$

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{sin}^{- 1} x - {sin}^{- 1} y = \frac{2 π}{3}; {cos}^{- 1} x - {cos}^{- 1} = \frac{π}{3}

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