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In an acute-angled triangle ABC, tanA+ta...

In an acute-angled triangle ABC, `tanA+tanB+tanC=tanAtanBtanC`, then
`tanAtanBtanC` =

A

`ge3`

B

`gesqrt3`

C

`ge3sqrt3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
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`
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