If sin - 1 x + sin - 1 y = 2 3 , then the value of cos - 1 x + cos - 1 y will be:

Question

If $\sin^{- 1} x + \sin^{- 1} y = \frac{2 π}{3},$ then the value of $\cos^{- 1} x + \cos^{- 1} y$ will be:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{π}{3}$

Explanation:

$\sin^{- 1} x + \sin^{- 1} y = \frac{2 π}{3}$

$\Rightarrow (\frac{π}{2} - \cos^{- 1} x) + (\frac{π}{2} - \cos^{- 1} y) = \frac{2 π}{3}$ $(∵ \sin^{- 1} x + \cos^{- 1} x = \frac{π}{2})$

$\Rightarrow$ $π - \frac{2 π}{3} = \cos^{- 1} x + \cos^{- 1} y$

$∴$ $\cos^{- 1} x + \cos^{- 1} y = \frac{π}{3}$

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