Question

Tan 3 theta / tan theta =4 then sin 3 theta/ sin theta is

Answer 1

Step-by-step explanation:

We have,

$\dfrac{\tan 3\theta}{\tan \theta} =4$

To find, the value of $\dfrac{\sin 3\theta}{\sin \theta}$ = ?

Using the trigonometric identity,

$\tan 3A=\dfrac{3\tan A-\tan^3 A}{1-3\tan^2 A}$

∴ $\dfrac{\tan 3\theta}{\tan \theta} =4$

⇒ $\dfrac{\dfrac{\tan \theta(3-\tan^2 \theta)}{1-3\tan^2 \theta} }{\tan \theta}$ = 4

⇒ $3-\tan^2 \theta=4(1-3\tan^2 \theta)$

⇒ $3-\tan^2 \theta=4-12\tan^2 \theta$

⇒ $11\tan^2 \theta=1$