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Trig Functions question

  1. Apr 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Simplify: cosx / (1+sinx)

    2. The attempt at a solution

    1 / (sec x)(1+sin x)

    1 / (sec x + (sin x / cos x))

    1 / (sec x + tan x)

    I know that the answer is sec x - tan x but don't know how to get there.

    Any help would be appreciated.
  2. jcsd
  3. Apr 9, 2007 #2
    Do you know what the value of [tex]sec^2x-tan^2x[/tex] is?

    The difference of two squares helps too.
  4. Apr 9, 2007 #3
    sec^2 (x) - tan^2 (x) = 1

    but nothing's squared in the problem
  5. Apr 9, 2007 #4
    Not until you do some multiplying.

    Do you understand what I mean by the difference of two squares?
  6. Apr 9, 2007 #5


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    You could also just multiply top and bottom of your given expression by (1-sin(x)) and expand. It's really the same thing as jing is suggesting.
  7. Apr 9, 2007 #6
    OK, So it's

    (sec x - tan x) / (sec x + tan x)(sec x -tan x)

    = (sec x - tan x) / 1

    = sec x -tan x

    Thank you so much!!
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