Bagaimana cara membuktikan sin2x – sin2y = sin(x + y)sin(x – y)?
Kita harus membuktikan (sin (x+y)sin (xy)=sin^{2}x-sin^{2}y)
Larutan
Mari kita mulai dengan RHS
(sin (x+y)sin (xy))
=((sin x cos y+ cos x sin y)(sin x cos y – cos x sin y))
=((sin ^{2}xcos ^{2}y-cos ^{2}xsin ^{2}y))
=(sin ^{2}x(1-sin ^{2}y)-(1-sin ^{2}x)sin ^{2}y)
=(sin ^{2}-sin ^{2}y)
= LHS
Maka Terbukti
