Question

How do you prove `(cosx - sinx - cos^3x)/cosx = sin^2x - tanx`?

`(cosx - sinx - cos^3x)/cosx = sin^2x - tanx`

Answer 1

`LHS=(cosx-sinx-cos^3x)/cosx`

`=cosx/cosx-sinx/cosx-cos^3x/cosx`

`=1-tanx-cos^2x=sin^2x-tanx=RHS`