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If ` y=cos ^(-1) ((1-x^(2))/( 1+x^(2))) ,then (dy)/(dx)=`

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if `cos^(-1)((1-a^2)/(1+a^2)) - cos^(-1)((1-b^2)/(1+b^2)) = 2tan^(-1)x` then x is:

prove that `cos^-1 x = 2 sin^-1 sqrt((1-x)/2) = 2 cos^-1 sqrt((1+x)/2) `

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