Trigonometric identity

Discussion in 'Math' started by boks, Nov 27, 2008.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    Why is

    cos^2 x = \frac{1}{2} + \frac{cos(2x)}{2}

    ?
     
  2. vvkannan

    Active Member

    Aug 9, 2008
    138
    11
    From the identity
    cos(x+y)=cosxcosy-sinxsiny
    Now if x=y
    cos 2x=cos^2 x - sin ^2 x
    cos 2x=cos ^2 x- (1-cos^2 x)
    cos 2x=2 cos^2 x - 1
    cos ^2 x= (1+cos 2x)/2
     
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