Question

Buktikan identitas : (sin x + cos x)2 - (sin x - cos x)2= 4 sin x cos x

Answer 1

(sin x + cos x)² - (sin x - cos x)²
= (sin² x + cos² x + 2 sin x cos x) - (sin² x + cos² x - 2 sin x cos x)
= sin² x + cos² x + 2 sin x cos x - sin² x - cos² x + 2 sin x cos x
= sin² x - sin² x + cos² x - cos² x + 2 sin x cos x + 2 sin x cos x
= 0 + 0 + 4 sin x cos x
= 4 sin x cos x ⇔ Terbukti