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Math Help - double angle formulas

  1. #1
    Junior Member
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    double angle formulas

    I was wondering if anyone can tell me how the following identity is derived:

    double angle formulas-screen-shot-2010-06-24-10.52.51.png

    Thank you
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  2. #2
    MHF Contributor
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    Quote Originally Posted by maggiec View Post
    I was wondering if anyone can tell me how the following identity is derived:

    Click image for larger version. 

Name:	Screen shot 2010-06-24 at 10.52.51.png 
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    Thank you
    Start with

    sin (p+q) - sin (p-q) = sin p cos q+cos p sin q-sin p cos q+cos p sin q

    = 2 cos p sin q

    Now let p+q=a ---1 and p-q=b ----2

    1+2 2p=a+b implies p=(a+b)/2

    1-2 2q=a-b implies q=(a-b)/2

    Hence sin p-sin q=2 cos (a+b)/2 sin (a-b)/2
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