First slide

Multiple and sub- multiple Angles

Question

Given that a, b, c are the sides of a $∆$ ABC which is right angled at C, then the minimum value of ${(\frac{c}{a} + \frac{c}{b})}^{2}$ is

Moderate

A

0
B

4
C

6
D

8

Solution

$\begin{array}{l} a = csin θ, b = ccos θ \\ \Rightarrow {(\frac{c}{a} + \frac{c}{b})}^{2} = {(\frac{1}{\sin θ} + \frac{1}{\cos θ})}^{2} = \frac{4 (1 + \sin 2 θ)}{\sin^{2} 2 θ} \\ = 4 (\frac{1}{\sin^{2} 2 θ} + \frac{1}{\sin 2 θ}), where 0 < θ < \frac{π}{2} \\ \Rightarrow {(\frac{c}{a} + \frac{c}{b})}_{min}^{2} = 8, when 2 θ = 90^{\circ} . \end{array}$

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