Home » Uncategorized » Trigonometric inequality on a triangle

# Trigonometric inequality on a triangle

Let be a triangle. Prove that

Solution

The function is convex, thus:

The result follows. In fact, something a bit stronger holds. Let denote the inradius , the circumradius and the semiperimeter. Then,

Indeed,

in view of the known identities

(1)

(2)

(3)

## 1 Comment

### Who is Tolaso?

Find out more at his Encyclopedia Page.