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Math Help - Trig Equation Confusion

  1. #1
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    Trig Equation Confusion

    Hi,
    First off I know how to do things such as,

    cosx x cos 4x = (1/2) x (cos(x+4x) + cos(x-4x))
    = (1/2) x (cos 5x) x (cos(-3x))

    However i'm getting very confused over one simple difference which is,

    2 sin5x . sin2x, as in what do I with the 2 out the front of this equation?

    This is what I tried (I have no idea though if its right or wrong)

    (2 sin5x . sin2x) = (1/2)x(2) x (sin(5x+2x) + (cos5x-2x))
    = (sin 7x) + (cos3x)

    Any help would be great.
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  2. #2
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    The cos product identity is (where * denotes multiplication and / denotes division)
    cos(x)*cos(y) = (cos(x+y) + (cos(x-y))/2

    The sin product identity is
    sin(x)*sin(y) = (cos(x-y) - (cos(x+y))/2

    You cannot simply replace cos with sin.

    so for your equation
    2*(sin(5x)*sin(2x)) we need to use the sin product identity.

    We will first tackle the (sin(5x)*sin(2x)) and after we solve for that, we will substitute it into the original equation

    sin(5x)*sin(2x)= (cos(5x-2x)-cos(5x+2x))/2 = (cos(3x)-cos(7x))/2

    Plug this back into your equation for (sin(5x)*sin(2x)) and you have 2*((cos(3x)-cos(7x))/2) where the 2s cancel out and you have

    = cos(3x)-cos(7x)
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  3. #3
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    Help on doubles angles

    Plz help me to understand double angles
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by kitty View Post
    Plz help me to understand double angles
    Please start a new thread for this , if you have problems in starting them , ask it
    btw here is a general answer to that question, we cant teach you that , but we can give links to useful sites
    http://en.wikipedia.org/wiki/Proofs_...ric_identities
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