If 3 2 -3=0 then =? - Vidyadip

MCQ

If $\sqrt{3} \tan 2 \theta-3=0$ then $\theta=?$

✓
$30^{\circ}$
B
$60^{\circ}$
C
$15^{\circ}$
D
$45^{\circ}$

✓

Answer

Correct option: A.

$30^{\circ}$

$\sqrt{3} \tan 2 \theta-3=0$
$\Rightarrow \sqrt{3} \tan 2 \theta=3$
$\Rightarrow \tan 2 \theta=\frac{3}{\sqrt{3}}$
$\Rightarrow \tan 2 \theta=\sqrt{3}$
$\Rightarrow \tan 2 \theta=\tan 60^{\circ}$
$\Rightarrow 2 \theta=60^{\circ}$
$\Rightarrow \theta=30^{\circ}$

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