If `u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))`

Explanation

To solve the problem, we need to show that

\[ \frac{du}{dv} = \sqrt{\frac{1 - u^2}{1 - v^2}} \]

where \( u = \sin(m \cos^{-1}(x)) \) and \( v = \cos(m \sin^{-1}(x)) \).

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