Find the range of the function $cos ({sin}^{- 1} x + {cos}^{- 1} x)$ for $| x | < 1$ .

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Solution

We've for ${sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2}$ for $| x | < 1$ .
Now,
$cos ({sin}^{- 1} x + {cos}^{- 1} x)$
$= cos \frac{π}{2}$
$= 0$ .
So range of the given function is ${0}$ .

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