Question

In an acute-angled triangle ABC, `tanA+tanB+tanC`
A. `ge3`
B. `gesqrt3`
C. `ge3sqrt3`
D. none of these

Answer 1

Correct Answer - C
In `DeltaABC,` we have
`tanA +tanB+tanC=tanAtanBtanC" "...(i)`
But, `A.M geG.M.`
`implies(tanA+tanB+tanC)/(3)ge(tanAtanBtanC)^(1//3)`
`implies((tanAtanBtanC)/(3))ge(tanAtanBtanC)^(1//3)" "["Using(i)"]`
`implies((tanAtanBtanC)/(3))^(2//3)ge1`
`impliestanAtanB tanCge3^(3//2)`
`tan A tanBtanCge3sqrt3`