Question

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

• A. \(30^\circ\)
• B. \(45^\circ\)
• C. \(60^\circ\)
• D. \(90^\circ\)

Hint:

In \(0^\circ\)–\(90^\circ\), \(\sin\theta=\cos\theta\) only at \(\theta=45^\circ\).

Answer 1

The Correct Option is B

Step 1: Use equality.
\(\sin\theta=\cos\theta\Rightarrow \tan\theta=1\).
Step 2: Principal value in first quadrant.
\(\theta=45^\circ\).