Question

If \( \sin \theta = \cos \theta \), \( 0^\circ \leq \theta \leq 90^\circ \), then the value of \( \theta \) is:

• A. 60°
• B. 45°
• C. 30°
• D. 0°

Hint:

The angle \( \theta \) for which \( \sin \theta = \cos \theta \) in the range \( 0^\circ \leq \theta \leq 90^\circ \) is \( 45^\circ \).

Answer 1

The Correct Option is B

We are given that \( \sin \theta = \cos \theta \) and \( 0^\circ \leq \theta \leq 90^\circ \).
Step 1: Use the identity for sine and cosine.
We know that: \[ \sin \theta = \cos \theta \] This occurs when \( \theta = 45^\circ \), as at \( 45^\circ \), both \( \sin 45^\circ \) and \( \cos 45^\circ \) have the same value: \[ \sin 45^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2} \]
Step 2: Conclusion.
Therefore, the value of \( \theta \) is 45°. The correct answer is (B).