Question

If $\sqrt{3}\tan \theta =1$ and $\theta$ is acute, find the values of $\sin 3\theta$ and $\cos 2\theta$

Answer 1

Given $\sqrt{3}\tan \theta =1\Rightarrow \tan \theta =\frac{1}{\sqrt{3}}$
We know $\tan {30}^o=\frac{1}{\sqrt{3}}\therefore \tan \theta ={30}^o\therefore \theta ={30}^o$
$\therefore 2\theta =2\times {30}^o={60}^o$ and $3\theta =3\times {30}^o={90}^o$
$\therefore \sin 3\theta =\sin {90}^o=1$ $\cos 2\theta =\cos {60}^o=\frac{1}{2}$