If A, B, C are the angles of an acute angled triangle, then cot(A/2) . cot(B/2) . cot(C/2) ≥

Question

If A, B, C are the angles of an acute angled triangle, then cot^{\(\frac{A}2\)} . cot^{\(\frac{B}2\)} . cot^{\(\frac{C}2\)} ≥

(a) 4√3 

(b) 8 

(c) 3√3 

(d) 3

Answer 1

A, B, C being the angles of an acute angled triangle, 

A + B + C = π

A, B, C are acute angles, tan A > 0, tan B > 0, tan C > 0 

Also, A + B + C = π ⇒ \(\frac{A}2+\frac{B}2+\frac{C}2=\frac{π}{2}\)

Applying AM – GM inequality, we have