If A>0,B>0 and A+B=π6then the minimum value of tan⁡A+tan⁡B is

If A>0,B>0 and A+B=π6then the minimum value of tanA+tanB is

  1. A

    32

  2. B

    423

  3. C

    23

  4. D

    23

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    Solution:

    We know that, tan(A+B)=tanA+tanB1tanAtanB

    13=y1tanAtanB, where y=tanA+tanBtanAtanB=13y

    Also  A.M.  G.M. 

    tanA+tanB2tanAtanBy213yy2443yy2+43y40y234 or y23+4

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