First slide

Multiple and sub- multiple Angles

Question

If $\cos (α - β) = 3 \sin (α + β), then \frac{1}{1 - 3 \sin 2 α} + \frac{1}{1 - 3 \sin 2 β} =$

Moderate

A

$\frac{1}{2}$
B

$- \frac{1}{2}$
C

$\frac{1}{4}$
D

$- \frac{1}{4}$

Solution

$put β = 0 \Rightarrow \tan α = \frac{1}{3}$
$\begin{array}{l} \Rightarrow \sin 2 α = \frac{2 (\frac{1}{3})}{1 + \frac{1}{9}} = \frac{3}{5} \\ ∴ \frac{1}{1 - 3 \sin 2 α} + \frac{1}{1 - 3 \sin 2 β} \\ = \frac{1}{1 - 3 \sin 2 α} + 1 = \frac{1}{1 - \frac{9}{5}} + 1 = \frac{- 1}{4} \end{array}$

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