Home
Class 11
MATHS
In an acute angled triangle ABC, the min...

In an acute angled `triangle ABC`, the minimum value of `tanA tanB tanC` is

Text Solution

Verified by Experts

As, `tanA*tanB*tanC= tanA+ tanB + tanC` Since, `A.M ge G.M` `(tanA+ tanB + tanC)/3 ge root(3)(tanA*tanB*tanC)` `root(2/3)(tanA+ tanB + tanC) ge 3` So, `(tanA + tanB+ tanC) ge 3^(3/2)` Hence,` min(tanA + tanB+ tanC)= 3sqrt3`
Promotional Banner

Similar Questions

Explore conceptually related problems

In an acute angled Delta ABC, the minimum value of tanAtanBtanc is

Statement-1: In an acute angled triangle minimum value of tan alpha + tanbeta + tan gamma is 3sqrt(3) . And Statement-2: If a,b,c are three positive real numbers then (a+b+c)/3 ge sqrt(abc) into in a triangleABC , tanA+ tanB + tanC= tanA. tanB.tanC

Statement-1: In an acute angled triangle minimum value of tan alpha + tanbeta + tan gamma is 3sqrt(3) . And Statement-2: If a,b,c are three positive real numbers then (a+b+c)/3 ge sqrt(abc) into in a triangleABC , tanA+ tanB + tanC= tanA. tanB.tanC

In an acute-angled triangle ABC, tanA+tanB+tanC

In an acute-angled triangle ABC, tanA+tanB+tanC

In triangle ABC, prove that the maximum value of tanA/2tanB/2tanC/2i s R/(2s)

In triangle ABC, prove that the maximum value of tanA/2tanB/2tanC/2i s R/(2s)

In triangle ABC, prove that the maximum value of tanA/2tanB/2tanC/2i s R/(2s)

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

Find the value of tanA+tanB+tanC , if A+B+C=pi :