Simplify the expression by using a sum or difference identity.
-sin (59°) cos(41°) + sin(-31°) sin(-41°)
A) cos 100°
B) 1
C) 0
D) sin 100°

Question

Quizplus · Accepted Answer

This expression can be simplified using the sum-to-product identities. Specifically, the identity sin(A)cos(B) + cos(A)sin(B) = sin(A + B) applies here, with A = 59° and B = -31°. Thus, sin(59°)cos(41°) + sin(-31°)sin(-41°) simplifies to sin(59° - 31°) = sin(28°), not directly matching any of the provided options. However, recognizing a mistake in my explanation, the correct approach should involve recognizing that sin(-31°) = -sin(31°) and sin(-41°) = -sin(41°), which actually simplifies correctly to sin(59° + 41°) = sin(100°), matching option D. My initial explanation mistakenly applied the wrong identities and arithmetic, leading to an incorrect simplification.

Simplify the Expression by Using a Sum or Difference Identity