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Question:

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then write the value of $x+y+z$

Solution:

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

$\Rightarrow \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{\pi}{2}+\frac{\pi}{2}+\frac{\pi}{2}$

$\left[\right.$ As the maximum value in the range of $\sin ^{-1} x$ is $\frac{\pi}{2}$ And here sum of three inverse of sine is 3 times $\frac{\pi}{2}$. i. e., every sin inverse function is equal to $\frac{\pi}{2}$ here. $] \Rightarrow \sin ^{-1} x=$