Question

How do you prove the identity `(sin^3 x + cos^3 x)/(sin x +cos x) = 1 - sin x cosx`?

Answer 1

Prove trig identity.

Explanation:

Use algebraic identity: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

`((sin x + cos x)(sin^2 x - sin x.cos x + cos^2 x))/(sin x + cos x)`

`= sin^2 x + cos^2 x - sin x.cos x = 1 - sin x.cos x`