Question

simplify ->
cos-1(1-x^2n/1+x^2n)

Answer 1

Put xn=tan(θ)xn=tan(θ)

cos−11−x2n1+x2ncos−11−x2n1+x2n

=cos−11−tan2θ1+tan2θ=cos−11−tan2θ1+tan2θ

=cos−1cos2θ−sin2θcos2θ+sin2θ=cos−1cos2θ−sin2θcos2θ+sin2θ

=cos−1(cos 2θ)=cos−1(cos 2θ)

=2θ=2θ

=2tan−1(xn)=2tan−1(xn)

So, derivative will be

2nxn−11+x2n,2nxn−11+x2n,

according to chain rule.