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If A, B, C be an acute angled triangle, then the minimum value of `tan^(4)A+tan^(4)B+tan^(4)C` will be

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If A, B, C be an acute angled triangle, then the minimum value of `tan^(4)A+tan^(4)B+tan^(4)C` will be
A. 729
B. 27
C. `81sqrt3`
D. none of these
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1 Answer

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Best answer
Correct Answer - B
In a triangle ABC, we know that
`tanA+tanB+tanCge3sqrt3" "...(i)`
We also know that
`(tan^(4)A+tan^(4)B+tan^(4)C)/(3)ge((tanA+tanB+tanC)/(3))^(4)`
`implies(tan^(4)A+tan^(4)B+tan^(4)C)/(3)ge(sqrt3)^(4)" "["Using(i)"]`
`impliestan^(4)A+tan^(4)B+tan^(4)C ge27`
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