Question

Given $\sqrt{3}\tan \theta =1$ and $\theta$ is an acute angle. Find the value of $\sin 3\theta$

Answer 1

$\sqrt{3}\tan \theta =1$
$\tan \theta =\frac{1}{\sqrt{3}}$
We know that $\tan {30}^{\circ }=\frac{1}{\sqrt{3}}\therefore \theta ={30}^{\circ }$
$\therefore \sin 3\theta =\sin 3\left({30}^{\circ }\right)$
$\sin 3\theta =\sin {90}^{\circ }=1$.