First slide

Extreme values and Periodicity of Trigonometric functions

Question

$The least value of \sec A + \sec B + \sec C in a acute angled triangle$

Difficult

A

$- \frac{1}{8}$
B

$\frac{3 \sqrt{3}}{2}$
C

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

6

Solution

$In Δ A B C, A, B, C are acute.$
$\Rightarrow \sec A, \sec B, \sec C are positive$
$Now, A \cdot M \geq H \cdot M .$
$\frac{\sec A + \sec B + \sec C}{3} \geq \frac{3}{\cos A + \cos B + \cos C} \to (1)$
We have $\frac{\cos A + \cos B + \cos C}{3} \leq \cos (\frac{A + B + C}{3})$
$\leq \cos 60 °$
$∴ \cos A + \cos B + \cos C \leq \frac{3}{2}$ $\to (2)$
From (1) and (2)
$\sec A + \sec B + \sec C \geq 6$

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