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Math Help - Proving

  1. #1
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    Proving

    Prove  <br />
cos (2x+x) = 4cos^3x - 3cosx<br />
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  2. #2
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    Dear punch,

    First expand Cos(2x+x) using,

    Cos{(2x+x)}=Cos{2x}Cos{x}-Sin{2x}Sin{x}

    Then use Cos2x=2Cos^2x-1\mbox{ and }{Sin^2}x=1-{Cos^2}x
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  3. #3
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    Quote Originally Posted by Punch View Post
    Prove  <br />
cos (2x+x) = 4cos^3x - 3cosx<br />

    cos(2x+x)=cos(2x)cos(x)-sin(2x)sin(x)

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

    =2cos^3(x)-cos(x)-2cos(x)(1-cos^2(x))

    =2cos^3(x)-cos(x)-2cos(x)+2cos^3(x)

     <br />
=4cos^3(x)-3cos(x)<br />
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  4. #4
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    Oh, thanks a lot guys, i was thinking about the extra sin^2 i had, now i know how to get rid of it by using identities...
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