The range of $a r c sin x + a r c cos x + a r c tan x$ is

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Solution

Let, $y = {sin}^{- 1} x + {cos}^{- 1} x + {tan}^{- 1} x$
or, $y = \frac{π}{2}$ $+ {tan}^{- 1} x$ . [Since ${sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2}$ ]
As range of ${tan}^{- 1} x$ is $(- \frac{π}{2}, \frac{π}{2})$ , so range of $y$ is $(0, π)$ .

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