If `x,y,z` be all positive acute angles then the least value of `tanx(coty+cotz)+tany(cotz+cotx)+tanz(cotx+coty)` is

Options

A. 2
B. 4
C. 6
D. 8

Answer

C

Explanation

`E = tan x(cot y+cot z)+tan y(cot z+cot x)+tan z (cot x + cot y)`
Using A.M. `ge G.M.`
`{:(tan x cot y + tan x cot z),(" "+tan y cot z + tan y cot x),(" "+tan z.cot x.tan z.cot y),(bar(" 6 ")),(" "ge tan x.cot y.tan x.cot z),(" "xx tan y.cot z. tan x. cot z),(" "xx tan y. cot z. tan y. cot x),(" "xx tan z. cot x. tan z. cot y):}`
`therefore E ge 6`