Question

Given the expression $\sin(3x + 10^{\circ}) = \cos(2x - 10^{\circ})$, which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of $x$?Answer Choices$36^{\circ}$$18^{\circ}$$22^{\circ}$$16^{\circ}$

Answer 1

Use sin A = cos B = sin(90° − B). Let A = 3x + 10° and B = 2x − 10°. Then

3x + 10° = 90° − (2x − 10°) + 360°k = 100° − 2x + 360°k.

So 5x = 90° + 360°k, hence x = 18° + 72°k. The solution in the given choices is 18°.