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Math Help - Sum and Difference Formulas PROVE

  1. #1
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    Sum and Difference Formulas PROVE

    Given this formula

    Sum
    sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

    prove this one
    Difference
    sin(a-b)=sin(a)*cos(b)-cos(a)*sin(b)

    Given this formula

    Sum
    cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)

    prove this one
    Difference
    cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)


    I assume it's the same concept for both of them, i just don't know how to go about proving it to be true.
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  2. #2
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    Talking

    My guess is that you're supposed to let sin(a - b) = sin(a + (-b)), and then use the fact that sin(-x) = -sin(x).
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  3. #3
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    Quote Originally Posted by stapel View Post
    My guess is that you're supposed to let sin(a - b) = sin(a + (-b)), and then use the fact that sin(-x) = -sin(x).
    Hmm, could you elaborate?

    EDIT: solved, thank you for the hint
    Last edited by ryno16; November 9th 2009 at 06:42 AM.
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  4. #4
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    No longer necessary.
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  5. #5
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    given that,
    sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

    prove
    sin(a-b)
    = sin(a+(-b))
    = sin(a)*cos(-b)+cos(a)*sin(-b)
    __________________________
    cos(-b)= cos (b),
    sin(-b)= -sin (b).
    ------------------------------
    = sin(a)*cos(b)-cos(a)*sin(b)
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  6. #6
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    Quote Originally Posted by pencil09 View Post
    given that,
    sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

    prove
    sin(a-b)
    = sin(a+(-b))
    = sin(a)*cos(-b)+cos(a)*sin(-b)
    __________________________
    cos(-b)= cos (b),
    sin(-b)= -sin (b).
    ------------------------------
    = sin(a)*cos(b)-cos(a)*sin(b)
    Then for solving/proving the second equation, how would i go about performing that? In the same manner?
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