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Homework Help: How to simplify following trignometric expression

  1. Jul 26, 2013 #1
    1. The problem statement, all variables and given/known data

    - 1/[cosx(cos(x-90))]

    3. The attempt at a solution

    = - 1/[cosx(-cos(90-x))] //so first I take the negative sign out from (x-90) to make it (90-x)
    = +1/[cosx(cos(90-x))] // negative sign from outside the cos and outside the entire fraction combine to become positive
    = 1/[cosx(sinx)] //because cos(x-90) = sinx

    However this answer is incorrect the answer in the back states the following:

    = -1/[cosx(sinx)] //essentially the same except a negative sign infront of the fraction instead of positive. Why is that though? Can someone please help?
  2. jcsd
  3. Jul 26, 2013 #2


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    Staff: Mentor

    ##\cos(-x)=\cos(x)##, therefore ##\cos(x-90) = \cos(90-x)##.
  4. Jul 26, 2013 #3
    Oh yes that completely slipped my mind. Thank you Dr Claude!
  5. Jul 26, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Do you mean ##\cos(x) \cos(x-90)?## If so, write it as cos(x)*cos(x-90), because what you wrote could well mean something else, such as
    [tex] \cos\left( x \cos(x-90)\right)[/tex]
    or something similar.
  6. Jul 26, 2013 #5
    Duly noted thanks for the tip!
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