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Math Help - solving a trig problem

  1. #1
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    solving a trig problem

    Give all radian solutions to

    cos(7x)cos(2x) + sin(7x)sin(2x) = 1/2


    The only place where i know where to begin is

    cos(2x) = 2cos^2 - 1


    would i need to reduce the cos(7x) like

    cos(7x) = cos(4x + 3x)
    until i get down to cos(2x)?
    so i could use the identity

    Can anyone help me get started on this beast?
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  2. #2
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    Re: solving a trig problem

    Remember the identity cos ( A-B) = cos A cos B + sin A sin B use it and we have cos 5x = 1/2 now you can complete the solution.
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  3. #3
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    Re: solving a trig problem

    would i then use cos(5x) = cos(3x + 2x) is that the way to go?

    or would i use arccos?
    5x = arccos(1/2)
    Last edited by icelated; August 20th 2013 at 11:26 PM.
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  4. #4
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    Re: solving a trig problem

    No as mentioned the identity is cos ( A-B) = cos A cos B + sin A sin B
    What we have is
    LHS = cos(7x)cos(2x) + sin(7x)sin(2x) = cos ( 7x - 2x ) = cos 5X
    thus we get cos 5x = 1/2
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