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Math Help - In △ABC, prove that-

  1. #1
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    jharkhand
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    In △ABC, prove that-

    1. tan (B+C)=-tan A

    2. cos (B+C)/2 = sin A/2
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  2. #2
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    Hello snigdha
    Quote Originally Posted by snigdha View Post
    1. tan (B+C)=-tan A

    2. cos (B+C)/2 = sin A/2
    First, note that:
    \tan(180^o-\theta) = -\tan\theta
    and
    \cos(90^o-\theta) = \sin\theta
    1.
    A+B+C = 180^o

    B+C = 180^o-A

    \Rightarrow \tan(B+C) = \tan(180^o-A)
    =-\tan A
    2.
    B+C = 180^o-A

    \Rightarrow \tfrac12(B+C) = 90^o-\tfrac12A

    \Rightarrow \cos\tfrac12(B+C) = \cos(90^o-\tfrac12A)
    =\sin\tfrac12A
    Grandad
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