Question

Buktikan identitas trigonometri berikut : sin^3 x + cos^3 x / 1-sin x . cos x = sin x + cos x

Answer 1

Sin^3 x + cos^3 x ={ (sin^2 x + cos^2 x ) (sin x + cos x) } - (sin^2 x cos x + cos^2 x sin x)
= 1 (sin x + cos x) - (sin x cos x (sin X + cos x )
= sin x + cos x (1 - sin x cos x ) dibagi 1 - sin x cos x = sin x + cos x (terbukti)