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Properties Derived from Trigonometric Identities

If cos -1 x...

Question

If ${cos}^{- 1} x + {cos}^{- 1} y = \frac{π}{2}$ , then prove that ${cos}^{- 1} x = {sin}^{- 1} y$

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Solution

${cos}^{- 1} x + {cos}^{- 1} y = \frac{π}{2}$
${cos}^{- 1} x = \frac{π}{2} - {cos}^{- 1} y$
$∵ {sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2}$
Hence, ${cos}^{- 1} x = {sin}^{- 1} y$

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Properties Derived from Trigonometric Identities

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