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  4. If cos-1 x + cos-1 y = π, then, what is the value of sin-1x + sin-1y ?

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Q. If $\cos^{-1} x + \cos^{-1} y = \pi,$ then, what is the value of $ \sin^{-1}x + \sin^{-1}y $ ?

Inverse Trigonometric Functions

Solution:

As given, $\cos^{-1} x + \cos^{-1} y = \pi$
Since, $ \sin^{-1}x +\cos^{-1}x = \pi /2$
and $ \sin^{-1}y + \cos^{-1}y = \pi/2$
$ \Rightarrow \frac{\pi}{2} - \sin^{-1} x + \frac{\pi}{2} - \sin^{-1} y = \pi $
$ \Rightarrow \pi- \left(\sin^{-1} x + \sin^{-1} y\right) =\pi $
$ \Rightarrow \sin^{-1} x + \sin^{-1}y = 0 $