Question

If $\frac{\tan 3\theta }{\tan \theta }=4$, then the value of $3\frac{\sin 3\theta }{\sin \theta }$ is.

Answer 1

Answer: 8

$\frac{\tan 3\theta }{\tan \theta }=4$
$\Rightarrow {\tan }^2\theta =\frac{1}{11}$
$\frac{\sin 3\theta }{\sin \theta }=3-4{\sin }^2\theta$
$=3\cdot 4\left(\frac{1}{1+{\cot }^2\theta }\right)=\frac{8}{3}$