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Math Help - Verifying trig identities?

  1. #1
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    Verifying trig identities?

    Okay, I've been getting some of these, but I can't seem to verify this identity... any help? Here's the problem

    Sin(x+y) + Sin(x-y) = 2sinxcosy

    Okay, I've been working on the left side, and distribute, getting:
    Sinx + Siny + Sinx - Siny

    And, the sinx's add up to the 2sinx that I need for the right side, but the siny's cancel out if I don't change them around. So I changed one of them to 1/cscy... but I can't seem to work with that and the other siny to end up with cosy.

    Where did I go wrong, or where do I go with it now?
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  2. #2
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    do not distribute

    use trig. formula for sin(x+y) and sin(x-y)

    sin(x+y) = sinx cosy + cosx siny
    sin(x-y) = sinx cosy - cosx siny

    now add

    try the following page for trigonometric identities
    mixture: trigonometric identities
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  3. #3
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    oh, dang, forgot about that identity!

    Okay, well, adding that up it ends up as 2sinx2cosy... but I need it to be 2sinx(1)cosy.

    or am I really tired and I'm thinking too out of the box to realize the entire term of 2sinxcosy consists of 2sinx's and 2cosy's?

    if not, what do I switch up to drop a cosy to satisfy the right side of the equation? oh man, am i sure forgetting everything about math, lol.
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  4. #4
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    Quote Originally Posted by a1b2c3 View Post
    oh, dang, forgot about that identity!

    Okay, well, adding that up it ends up as 2sinx2cosy...

    no ...
    sin(x+y) = sinx cosy + cosx siny
    sin(x-y) = sinx cosy - cosx siny
    -------------------------------
    sin(x+y) + sin(x-y) = sinxcosy + sinxcosy = 2sinxcosy
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