Question

How do you prove that `tan^2x = csc^2x * tan^2x - 1`?

Answer 1

Apply the identities `tantheta = sintheta/costheta` and `csctheta = 1/sintheta`.

`sin^2x/cos^2x = 1/sin^2x xx sin^2x/cos^2x - 1`

`sin^2x/cos^2x = 1/cos^2x - 1`

`sin^2x/cos^2x = 1/cos^2x - cos^2x/cos^2x`

Apply the identity `1 - cos^2x = sin^2x` (`sin^2x+ cos^2x = 1`).

`sin^2x/cos^2x = sin^2x/cos^2x`

`LHS = RHS`

Hopefully this helps!