First slide

Trigonometric transformations

Question

$If A + B + C = π then the minimum value of \tan^{2} \frac{A}{2} + \tan^{2} \frac{B}{2} + \tan^{2} \frac{C}{2}$

Moderate

A

0
B

1
C

2
D

3

Solution

$\begin{array}{l} In Δ A B C \frac{\tan^{2} \frac{A}{2} + \tan^{2} \frac{B}{2} + \tan^{2} \frac{C}{2}}{3} \geq \tan^{2} (\frac{A + B + C}{6}) \\ \geq 3 \cdot \frac{1}{3} \\ \geq 1 \end{array}$

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