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

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Answer 1 · 2015-07-03T03:04:51

Prove trig identity.

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

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

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

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