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Math Help - proof (compound angles) trig identities

  1. #1
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    proof (compound angles) trig identities

    hi ,im struggling with this question,all help greatly appreciated
    this is the proof question ..


    sin(A+B) / sin(A-B) = (tanA + tanB) / (tanA - tanB )
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  2. #2
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    Hello mike--1988
    Quote Originally Posted by mike--1988 View Post
    hi ,im struggling with this question,all help greatly appreciated
    this is the proof question ..


    sin(A+B) / sin(A-B) = (tanA + tanB) / (tanA - tanB )
    \frac{\sin(A+B)}{\sin(A-B)}=\frac{\sin A \cos B + \cos A \sin B}{\sin A \cos B - \cos A \sin B}

    Divide top and bottom by \cos A \cos B:
    =\frac{\dfrac{\sin A}{ \cos A} + \dfrac{\sin B}{\cos B}}{\dfrac{\sin A}{ \cos A} - \dfrac{\sin B}{\cos B}}

    =\frac{\tan A + \tan B}{\tan A - \tan B}
    Grandad
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