First slide

Multiple and sub- multiple Angles

Question

If $\tan (α - β) = \frac{\sin 2 β}{3 - \cos 2 β}$ , then

Moderate

A

$\tan α = 2 \tan β$
B

$\tan β = 2 \tan α$
C

$2 \tan α = 3 \tan β$
D

$3 \tan α = 2 \tan β$

Solution

we have
$\begin{matrix} \frac{\sin 2 β}{3 - \cos 2 β} = \frac{2 \sin β \cdot \cos β}{2 - 2 \cos 2 β + 1 + \cos 2 β} \\ = \frac{2 \sin β \cdot \cos β}{4 \sin^{2} β + 2 \cos^{2} β} \\ = \frac{\tan β}{1 + 2 \tan^{2} β} \\ = \frac{2 \tan β - \tan β}{1 + 2 \tan^{2} β} \\ = \tan (α - β) \end{matrix}$
$\begin{array}{l} ∴ \frac{\tan α - \tan β}{1 + \tan α \cdot \tan β} = \frac{2 \tan β - \tan β}{1 + 2 \tan^{2} β} \\ ∴ \tan α = 2 \tan β \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App