Question

Tunjukkan kebenaran setiap identutas trigonometri berikut.
Sin ( a+b ) sin ( a-b )= sin² a - sin² b

Pleaseeeee

Answer 1

Verified answer

Identitas Trigonometri.

sin α sin β = 1/2 [cos (α - β) - cos (α + β)]

sin (a + b) sin (a - b) = 1/2 [cos (a + b - a + b) - cos (a + b + a - b)]
= 1/2 (cos 2b - cos 2a)
= 1/2 [(1 - 2 sin² b) - (1 - 2 sin² a)]
= 1/2 (2 sin² a - 2 sin² b)
= sin² a - sin² b
Terbukti.