How to show sin^(-1)(x)=tan^(-1)((x)/(1-x^2)^(1/2)) ?

1 Answer
Jun 3, 2018

Let x=sintheta

So RHS=tan^-1(x/(1-x^2)^(1/2))

=tan^-1(sintheta/(1-sin^2theta)^(1/2))

=tan^-1(sintheta/(cos^2theta)^(1/2))

=tan^-1(sintheta/costheta)

=tan^-1tantheta

=theta=sin^-1x=LHS