Q64 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

If $2 \sin 2 \theta=\sqrt{3}$, then $\theta=$

  • A
    $15^{\circ}$
  • B
    $27^{\circ}$
  • Correct answer
    C
    $30^{\circ}$
  • D
    $40^{\circ}$

Solution

We are given that $\begin{aligned} & 2 \sin \theta=\sqrt{3} \Rightarrow \sin 2 \theta=\frac{\sqrt{3}}{2}=\sin \left(\frac{\pi}{3}\right) \\ & \Rightarrow 2 \theta=\frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{6} \Rightarrow \theta=30^{\circ}\end{aligned}$

Hence, the correct answer is option: 'C'.

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