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 θ = cos(90° − θ). Let θ = 3x + 10° and set 3x + 10° = 90° − (2x − 10°) (or the other sine identity giving x = 70°, which is not among the choices).

Solve:
3x + 10° = 90° − 2x + 10°
3x + 10° = 100° − 2x
5x = 90°
x = 18°

Answer: 18°.