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Math Help - Proof using Law of Sines

  1. #1
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    Proof using Law of Sines

    For any triangle ABC, even if B or C is an obtuse angle, a = b cos C + c cos B. Use the Law of Sines to deduce the "addition formula"

    sin (B + C) = sin B cos C + sin C cos B

    I got most of it but can't figure out the end.
    I replaced b with 2R sin B and c with 2R sin C

    so
    a = 2R sin B cos C + 2R sin C cos B
    a = 2R (sin B cos C + sin C cos B)
    a/2R = sin B cos C + sin C cos B
    sin A = sin B cos C + sin C cos B

    I don't know where to go from here
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  2. #2
    Junior Member
    Joined
    Aug 2011
    Posts
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    Re: Proof using Law of Sines

    Since A + B + C = 180 degrees in a triangle. A = 180 - (B + C). Sin A = Sin [180 - (B + C)] = Sin (B + C). Hope this is correct. MHF expert has to vouch this.
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