AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(2 \sin 2 \theta=\sqrt{3}\), then \(\theta=\)
- A \(15^{\circ}\)
- B \(27^{\circ}\)
- C \(30^{\circ}\)
- D \(40^{\circ}\)
Answer & Solution
Correct Answer
(C) \(30^{\circ}\)
Step-by-step Solution
Detailed explanation
We are given that \(\begin{aligned} & 2 \sin \theta=\sqrt{3} \Rightarrow \sin 2 \theta=\frac{\sqrt{3}}{2}=\sin \left(\frac{\pi}{3}\right) \\ & \Rightarrow 2 \theta=\frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{6} \Rightarrow \theta=30^{\circ}\end{aligned}\)
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