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Range of $\sin^{- 1} x - \cos^{- 1} x$ is

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Correct option is A

Let y=sin−1x−cos−1x=π2−2cos−1xSince 0≤cos−1x≤π ⇒-2π≤-2cos−1x≤0 ⇒π2-2π≤π2-2cos−1x≤0 ⇒−3π2≤y≤π2

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Range of sin−1x−cos−1x is

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Range of $\sin^{- 1} x - \cos^{- 1} x$ is