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Use trig identities to simplify an expression (has sins and cosines)

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Use fundamental identities to simplify the expression:

    (sinx)^2 - (cosx)^2
    ____________________
    (sinx)^2 - (sinx cosx)


    *note: it's a numerator and denominator. The underscore line is the fraction line.

    *note: The answer in the back of the book is "1 + cotx" but I would like to know how it got there.

    2. Relevant equations

    (sinx)^2 + (cosx)^2 = 1

    other trig identities


    3. The attempt at a solution

    (sinx)^2 - (cosx)^2
    _________________
    sinx(sinx - cosx)

    I factored out sinx out of the bottom, but I don't really see any identies that would simplify sinx-cosx. (I have a chart of identities.) I tried to simplify the top using the relevant identity I already listed.

    Thanks for any help!
     
    Last edited: Apr 28, 2012
  2. jcsd
  3. Apr 28, 2012 #2

    SammyS

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    Factor the numerator as a difference of squares.

    or ...

    Starting with the original expression, multiply the numerator and denominator by 1/sin2(x)
     
  4. Apr 29, 2012 #3
    Thanks. I got it now. :)
     
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