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Trig identities

  1. Aug 1, 2011 #1
    1. The problem statement, all variables and given/known data

    tan^2x - sin^2x = sin^2x*tan^2x

    2. Relevant equations





    3. The attempt at a solution

    This is how my teacher solved it.

    Sin^2x sin^2x
    ______ - ______
    Cos^2x 1

    sin^2x - cos^2x*sin^2x
    _________________________
    cos^2x

    = sin^2x (1-cos^2x)
    ___________________
    cos^2x

    =sin^2x *sin^2x
    ______________
    cos^2x


    thus giving the answer. I dont understand what happends on the third line. How can 1-cos^2x be bracketed if cos^2x*sin^2x are one term, even though they equal one, how can that equal 1-cos^2x?
     
  2. jcsd
  3. Aug 1, 2011 #2

    rock.freak667

    User Avatar
    Homework Helper

    Because in sin2x - cos2xsin2x, sin2x is common in both terms, thus it can be factored as sin2x(1-cos2x).

    If you expand the bracket you will get back sin2x - cos2xsin2x, sin2x.
     
  4. Aug 2, 2011 #3

    PeterO

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    Homework Helper



    In the third line, what happened was factorisation.
     
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