Question

How do you prove `tantheta - cottheta/ tantheta+cottheta= sin^2theta- cos^2theta`?

Answer 1

We cannot as the given identity is false

Consider the graph of the LHS
graph{tanx - cotx/tanx+cotx [-10, 10, -5, 5]}

Consider the graph of the RHS
graph{(sinx)^2- (cosx)^2 [-10, 10, -5, 5]}