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If $A > 0, B > 0$ and $A + B = Ï / 3$ then the maximum value of tan $A$ tan $B$ is

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detailed solution

Correct option is B

Let tan A tan B = x so tanâ¡(A+B)=tanâ¡(Ï/3)=3âtanâ¡A+tanâ¡B1âtanâ¡Atanâ¡B=3â3(1âx)=tanâ¡A+tanâ¡Bâ¤2tanâ¡Atanâ¡B=2xâ3(1âx)2â¤4xâ3x2â10x+3â¤0â(3xâ1)(xâ3)â¤0â13â¤xâ¤3

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If A > 0, B > 0 and A+B=Ï/3 then the maximum value of tan A tan B is

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Ready to Test Your Skills?

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If $A > 0, B > 0$ and $A + B = Ï / 3$ then the maximum value of tan $A$ tan $B$ is