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^{-1}((^{-1}x))+^{-1}((^{-1}x))= ___________.

Question

$sin^{- 1} (cos (sin^{- 1} x)) + cos^{- 1} (sin (cos^{- 1} x)) =$ ___________.

\frac{π}{2}

\frac{π}{4}

0

- \frac{π}{2}

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sin^{- 1} (cos (sin^{- 1} x)) + cos^{- 1} (sin (cos^{- 1} x)) =

___________.

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13 mins ago

Text solutionVerified

co s^{- 1} x = s i n^{- 1} 1 - x^{2}

∴ s in (co s^{- 1} x) = s in (s i n^{- 1} 1 - x^{2}) = 1 - x^{2}

Similarly,

cos (s i n^{- 1} x) = cos (co s^{- 1} 1 - x^{2}) = 1 - x^{2}

∴ s i n^{- 1} (cos (s i n^{- 1} x)) + co s^{- 1} (s in (co s^{- 1} x))

= s i n^{- 1} (1 - x^{2}) + co s^{- 1} (1 - x^{2})

= \frac{π}{2}

....

[s i n^{- 1} (θ) + co s^{- 1} (θ) = \frac{π}{2}]

Hence, the answer is option (A).

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