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Identity question

  • 25-05-2012 7:11pm
    #1
    Smythe
    Registered Users, Registered Users 2 Posts: 434 ✭✭


    In a worked example I have of an integration it states the integral of (cosx)^2 = the integral of (1 + cos2x)/2

    How is this equality reached?

    Is this a known identity, (cosx)^2 = (1 + cos2x)/2 ?

    Thank you.


Comments

  • #2
    Neodymium
    Registered Users, Registered Users 2 Posts: 179 ✭✭Neodymium


    Integral of (cosx)^2 = x/2 + sin2x/4 + c

    Integral of (1+cos2x)/2 = x/2 + sin2x/4 + c


  • #3
    ride-the-spiral
    Registered Users, Registered Users 2 Posts: 1,263 ✭✭✭ride-the-spiral


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

    2(cosx)^2 = cos(2x) + 1
    (cosx)^2 = (cos(2x) + 1)/2


  • #4
    Smythe
    Registered Users, Registered Users 2 Posts: 434 ✭✭Smythe


    Thanks guys!


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