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Exam
Triangle ABC has angles α,β,γ. What is the maximum value of
[sqrt{tan(α/2)*tan(β/2)+8} + sqrt{tan(β/2)*tan(γ/2)+8} + sqrt{tan(γ/2)*tan(α/2)+8}]^2
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- It is maximum if triangle is equilateral.
=> [ 3*sqrt (tan30*tan30 + 8) ]^2
= 9 * 25 / 3
= 75 - 11 years agoHelpfull: Yes(2) No(0)
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