In a triangle ABC, if cosA=cosB cosC,then tanB+tanC=

In a triangle ABC, if cosA=cosB cosC,then tanB+tanC=

  1. A

    tanA

  2. B

    2tanA

  3. C

    cotA

  4. D

    tan2A

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    Solution:

    cosB cosC=cosA=- cos(B+C)

    =-(cosB cosC-sinB sinC)

     2cosB cosC=sinB sinC

     tanB tanC=2

    But tanA tanB tanC =tanA+tanB+tanC

     2 tanA=tanA+tanB+tanC 

     tanB+tanC=tanA.

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