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    cardkiller13's Avatar
    cardkiller13 Posts: 1, Reputation: 1
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    #1

    Apr 30, 2012, 04:06 PM
    Can you help me verify this trigonometric identity?
    1 + cos(10y)=2cos^2(5y)
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    May 1, 2012, 05:48 AM
    Quote Originally Posted by cardkiller13 View Post
    1 + cos(10y)=2cos^2(5y)
    Remember the identy for cos(2a):

    cos(2x) = cos^2(a) - sin^2(a).

    And if you apply sin^2(a) + cos^2(a) = 1, you can turn this either:

    cos(2a) = 1-2sin^2(a), or
    cos(2a) = 2 cos^2(a) -1

    So you actually have three forms of identity for cos(2a). If you consider that your problem is asking about cos(10y), and that 10y = 2 x 5y, then you have

    1 + cos(2 x 5y).

    Try using the various forms of identities for cos(2a) with the above, and see if you can work it out.

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