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Trig proof, I am getting a neg instead of pos.

  1. Jul 12, 2011 #1
    1. The problem statement, all variables and given/known data

    [cscx/(1+cscx)] - [cscx/(1-cscx)] = 2 sec^2 x

    2. Relevant equations

    prove the left side equals the right side

    3. The attempt at a solution

    1. get common denominator and subtract, [cscx(1-cscx)-cscx(1+cscx)]/[(1+cscx)(1-cscx)]

    2. distribute cscx in numerator [cscx-csc^2 x-cscx-csc^2 x]/
    and multiply out denominator [1-csc^2 x]

    3. combine like terms numerator [-2csc^2x]/
    identity in denominator (cot^2 x)

    4. reciprocal of cot=1/tan, then divide num/dem (-2csc^2 x)(tan^2 x)

    5. change csc and tan to sin, cos [-2(1/sin^2 x)] [(sin^2 x)/(cos^2x)]

    6. cross cancel and multiply -2(1/cos^2 x) or -2sec^2 x

    I have checked this several times and cannot figure out why I get -2 instead of 2.
     
  2. jcsd
  3. Jul 12, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    1-csc(x)^2=(-cot(x)^2), isn't it?
     
  4. Jul 12, 2011 #3
    Thats it. Thanks.

    I knew I was overlooking something simple.
     
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