Question:
If $\sqrt{3} \tan 2 \theta-3=0$ then $\theta=?$
(a) 15°
(b) 30°
(c) 45°
(d) 60°
Solution:
As we know that,
$\tan 60^{\circ}=\sqrt{3}$
Thus,
if $\sqrt{3} \tan 2 \theta-3=0$
$\Rightarrow \sqrt{3} \tan 2 \theta=3$
$\Rightarrow \tan 2 \theta=\frac{3}{\sqrt{3}}$
$\Rightarrow \tan 2 \theta=\sqrt{3}$
$\Rightarrow 2 \theta=60^{\circ}$
$\Rightarrow \theta=30^{\circ}$
Hence, the correct option is (b).
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