First slide

Geometric progression

Question

$In a triangle ABC, A, B, C are in G.P with common ratio 2 then \frac{1}{b} + \frac{1}{c} - \frac{1}{a} is =$

Moderate

A

1
B

-2
C

3
D

0

Solution

$We have B = 2 A, C = 4 A \Rightarrow 7 A = π \Rightarrow A = π / 7$
$\begin{aligned} \to \frac{1}{b} + \frac{1}{c} - \frac{1}{a} = \frac{1}{2 R} [\frac{1}{\sin 2 A} + \frac{1}{\sin 4 A} - \frac{1}{\sin A}] = \frac{2 \sin A \sin 4 A + 2 \sin A \sin 2 A - 2 \sin 2 A \sin 4 A}{4 Rsin A \sin 2 A \sin 4 A} \\ = \frac{1}{4 R} [\frac{\cos 2 A - \cos 2 A + \cos A - \cos A}{\sin A \sin 2 A \sin 4 A}] = 0 \end{aligned}$

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