Question

If \(\sqrt{3} \sin \theta = \cos \theta\), then value of \(\theta\) is

• A. \(\sqrt{3}\)
• B. \(60^\circ\)
• C. \(\dfrac{1}{\sqrt{3}}\)
• D. \(30^\circ\)

Hint:

Convert all terms to a single trigonometric ratio (like \(\tan \theta\)) to simplify.

Answer 1

The Correct Option is B

Divide both sides by \(\cos \theta\): \[ \sqrt{3} \tan \theta = 1 \Rightarrow \tan \theta = \dfrac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ \] But this gives option (D) — let’s recheck: Oops! Actually: \[ \sqrt{3} \sin \theta = \cos \theta \Rightarrow \tan \theta = \dfrac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ \] So correct answer is (D) \(30^\circ\)