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if sin^-1x+sin^-1y=pi/2 then find cos^-1x+cos^-1y

\sin^{- 1} (x) + \sin^{- 1} (y) = \frac{π}{2} \Rightarrow \cos e c^{- 1} (\frac{1}{x}) + \cos e c^{- 1} (\frac{1}{y}) = \frac{π}{2}

\Rightarrow \frac{π}{2} - s e c^{- 1} (\frac{1}{x}) + \frac{π}{2} - s e c^{- 1} (\frac{1}{y}) = \frac{π}{2}

[Since,

\cos e c^{- 1} (x) + s e c^{- 1} (x) = \frac{π}{2}

]

\Rightarrow π - s e c^{- 1} (\frac{1}{x}) - s e c^{- 1} (\frac{1}{y}) = \frac{π}{2} \Rightarrow \frac{π}{2} = s e c^{- 1} (\frac{1}{x}) + s e c^{- 1} (\frac{1}{y}) \Rightarrow \frac{π}{2} = \cos^{- 1} (x) + \cos^{- 1} (y)

Thus,

\cos^{- 1} (x) + \cos^{- 1} (y) = \frac{π}{2}

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