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  4. If ( tan 3 θ/ tan θ)=4, then the value of 3 ( sin 3 θ/ sin θ) is.

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

Trigonometric Functions

Solution:

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