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Homework Help: Trig Identity Question

  1. Mar 30, 2012 #1

    foil out the center
    I get

    the -cos(x)sin(x)+cos(x)sin(x) cancels to 0 leaving


    then I'm lost...

    I know I can switch 1-cos^2(x) to sin^2(x) but that doesn't help because I get

    where am i going wrong?
  2. jcsd
  3. Mar 30, 2012 #2
    Are you sure? Looks to me like the +cos(x)sin(x) and the -cos(x)sin(x) cancel out to leave:
  4. Mar 30, 2012 #3
    I wrote my foil wrong
    foiling leaves me
    1-cos^2(x)-cos(x)sin(x)+cos(x)sin(x) - sin^2(x)
  5. Mar 30, 2012 #4
    Don't remove the parentheses until after you've foiled it out or you're going to lose a negative sign.

    Foiling 1-[(cos(x)+sin(x))(cos(x)-sin(x))], we get
    1-(cos^2(x)-cos(x)sin(x)+cos(x)sin(x)-sin^2(x)). Two of the terms cancel, yielding:

    Now try using those Pythagorean identities.
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