Question

If \( \sin(20^\circ + \theta) = \cos 30^\circ \), then the value of \( \theta \) is

• A. 30°
• B. 40°
• C. 50°
• D. 60°

Hint:

Use complementary angles and the identity \( \sin x = \cos(90^\circ - x) \) to simplify solving for unknown angles in trigonometric equations.

Answer 1

The Correct Option is B

Step 1: Using the identity \( \cos x = \sin(90^\circ - x) \), we find: \[ \cos 30^\circ = \sin(60^\circ) \] Step 2: Set the sine equation: \[ \sin(20^\circ + \theta) = \sin 60^\circ \] Step 3: Solve for \( \theta \): \[ 20^\circ + \theta = 60^\circ \Rightarrow \theta = 40^\circ \] Thus, the correct answer is \( \boxed{40^\circ} \).