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Trig identity that I'm missing

  1. Nov 17, 2012 #1
    I am trying to integrate -tan(x)sec^2(x) and getting -tan^2(x) / 2. When I put it in wolfram alpha it gets the same answer when I press show solution, but without pressing it it shows -sec(x)/2.

    So I am wondering, is it the case tan^2(x) = sec(x)?? I don't remember this as a correct trig identity


    Notice the difference in answer when you press for the show step by step solution
    Last edited: Nov 17, 2012
  2. jcsd
  3. Nov 17, 2012 #2


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    Education Advisor

    I'm reading (1/2)[-sec(x)]^2 + C, in which case they might've used [tan(x)]^2 = [sec(x)]^2-1
  4. Nov 17, 2012 #3
    Ahh I was misreading it, thanks.
  5. Nov 17, 2012 #4


    Staff: Mentor

    In indefinite integral can have different answers, depending on the technique that is used, but the answers can differ by at most a constant.

    When you integrated -tan(x)sec2(x) you got -(1/2)tan2(x). Wolfram's answer was -(1/2)sec2(x). Since sec2(x) = tan2(x) + 1, your answer and Wolfram's answer differ by a constant.
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