Question

If x, y, z be all positive acute angles, then the least value of tan x (cot y + cot z) + tan y (cot z + cot x) + tan z (cot x + cot y), is

(A) 2

(B) 4

(C) 6

(D) 8

Answer 1

Correct option (C)

Explanation:

tan x (cot y + cot z) + tan y (cot x + cot z) + tan z (cot x + cot y) (tan x cot y + tany cot x) + (tan x cot z + cot x tan z) + (tany cot z + coty tanz)

By AM ≥ GM

2 + 2 + 2 ≥ 6