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Thread: In △ABC, prove that-

  1. #1
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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:
    $\displaystyle \tan(180^o-\theta) = -\tan\theta$
    and
    $\displaystyle \cos(90^o-\theta) = \sin\theta$
    1.
    $\displaystyle A+B+C = 180^o$

    $\displaystyle B+C = 180^o-A$

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

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

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