Question

How do you prove `cosx-cosxsin^2x=cos^3x`?

Answer 1

Remember `sin^2x+cos^2x = 1` (Pythagorean)
and equivalently `sin^2x = 1-cos^2x`

`cos x - cos x sin^2x`

`= cos x (1-sin^2 x)`

`= cos x (cos^2 x)`

`= cos^3x`