If u-sin-mcos-1-x-v-cos-msin-1-x- prove that dfrac-du-dv-dfrac-sqrt-1-u-2-sqrt-1-v-2-

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If $u = sin (m {cos}^{- 1} x), v = cos (m {sin}^{- 1} x)$ , prove that $\frac{d u}{d v} = \frac{\sqrt{1 - u^{2}}}{\sqrt{1 - v^{2}}}$ .

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