Use a product-to-sum identity to rewrite the expression.
-sin 19° sin 31°
A) 0.5(cos (12°) + cos(50°))
B) 0.5(sin (12°) + sin(50°))
C) 0.5(sin(50°) - sin (12°))
D) 0.5(cos (12°) - cos(50°))

Question

Quizplus · Accepted Answer

The product-to-sum identity for sine is: sin(A)sin(B) = 0.5[cos(A-B) - cos(A+B)]. Here, A = 19° and B = 31°, so it becomes 0.5[cos(19°-31°) - cos(19°+31°)] = 0.5[cos(-12°) - cos(50°)] = 0.5[cos(12°) - cos(50°)].

Use a Product-To-Sum Identity to Rewrite the Expression