Question from Jeff, a student:

i cannot prove this trigonometric identity. please help!

(cos x)^3 – (sin x)^3 = (cos x –sin x) (1+cosxsinx)

Jeff,

Use of the fact that u^{3} - v^{3} = (u-v)(u^{2} + uv + v^{2}). (Just let u = cos x and v = sin x. It will come down to a familiar identity.)

Chris