This is a Test of Mathematics Solution Subjective 116 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

## Problem

If A, B, C are the angles of a triangle, then show that

## Solution:

We apply Jensen’s Inequality and Arithmetic Mean – Geometric Mean inequality here. Since cosine function is concave in the interval , we have

This implies

## Chatuspathi:

**What is this topic:**Properties of triangle**What are some of the associated concept:**Jensen Inequality, Arithmetic Mean-Geometric Mean Inequality**Where can learn these topics:**I.S.I. & C.M.I. Entrance Course of Cheenta, discusses these topics in the ‘Inequality’ module.**Book Suggestions: ‘**Secrets in

cos(π – x) = -cos(x). And also the question is wrong. It is 3/2 in the right hand side of the inequality(as of seventeenth edition. Pls make the changes