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`        if A+B+C=pi and A,B,,C are acute angles then prove that tanA+tanB+tanC>=33/2`
2 years ago

Arun
24739 Points
```							Using A.M. > = G.M.(tanA + tanB + tanC)/3 >= (tanA.tanB.tanC)^(1/3)=> tanA + tanB + tanC >= 3*(tanA + tanB + tanC)^(1/3)...(since in triangle sum of tangents of angles is equal to product of tangents)=> tanA + tanB + tanC >= 3(3)^(1/2)tanA + tanB + tanC = 3(3)^(1/2) impliesA.M. = G.M. and this means tanA = tanB = tanC=> A =B =C and hence triangle is equilateral, If we take triangle as equilateral;then all the angles are 60 degree, then tanA+ tanB + tanC = 3(3)^(1/2) RegardsArun (askIITians forum expert)
```
2 years ago
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Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions