Differentiate sin^-1 (2x/1+x^2) with respect to cos^-1(1-x^2/1+x^2).

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Differentiate sin^-1 (2x/1+x^2) with respect to
cos^-1(1-x^2/1+x^2)

Ashwini Kumar · Accepted Answer

Let x=tantHere, let fx=sin-12x1+x2=sin-12tant1+tan2t=sin-1sin2t=2tNow, dfxdt=d2tdt=2And let gx=cos-11-x21+x2=cos-11-tan2t1+tan2t=cos-1cos2t=2tNow, dgxdt=d2tdt=2∴dsin-12x1+x2dcos-11-x21+x2=dfxdgx=dfxdt×1dgxdt=22=1