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Confusion with product-to-sum trig identities

  1. Jul 9, 2013 #1
    I'm having some confusion with a couple trig identities. On wikipedia (http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities), the following two identities are listed:

    sinθcosβ = (1/2)[sin(θ+β) + sin(θ-β)]

    and

    sinβcosθ = (1/2)[sin(θ+β) - sin(θ-β)]

    I can see the difference between them if they are used with the same variables θ and β. But, how do you know which one is valid in any given situation? I find this a hard question to phrase, but I hope you can see my confusion. If you have sin x cos y, which identity can you apply? Does it matter? So long as you apply the other one to sin y cos x?
     
  2. jcsd
  3. Jul 9, 2013 #2

    Ackbach

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    Gold Member

    They're really the same identity - one of them being superfluous. If you swap the roles of the arguments, and use the fact that [itex]\sin(-x)=-\sin(x)[/itex], then you will see that they are the same.
     
    Last edited: Jul 9, 2013
  4. Jul 9, 2013 #3
    I see, thank you.
     
  5. Jul 9, 2013 #4

    Ackbach

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    Gold Member

    You're welcome!
     
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