dear student du=cos(mcos-1x)m-11-x2dv=-sin(msin-1x)m11-x2LHS=dudv=cos(mcos-1x)m-11-x2-sin(msin-1x)m11-x2=cos(mcos-1x)sin(msin-1x)RHS=1-u21-v2=1-sin2(mcos-1x)21-cos2(msin-1x)2=cos(mcos-1x)sin(msin-1x) regards

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dear student

d u = \cos (m \cos^{- 1} x) m \frac{- 1}{\sqrt{1 - x^{2}}} d v = - \sin (m \sin^{- 1} x) m \frac{1}{\sqrt{1 - x^{2}}} L H S = \frac{d u}{d v} = \frac{\cos (m \cos^{- 1} x) m \frac{- 1}{\sqrt{1 - x^{2}}}}{- \sin (m \sin^{- 1} x) m \frac{1}{\sqrt{1 - x^{2}}}} = \frac{\cos (m \cos^{- 1} x)}{\sin (m \sin^{- 1} x)} R H S = \sqrt{\frac{1 - u^{2}}{1 - v^{2}}} = \sqrt{\frac{1 - \sin^{2} (m \cos^{- 1} x)^{2}}{1 - \cos^{2} (m \sin^{- 1} x) 2}} = \frac{\cos (m \cos^{- 1} x)}{\sin (m \sin^{- 1} x)}

regards

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