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(sec(x)+1)/tan(x) = (sin(x))/(1-cos(x))

  1. Mar 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove.

    (sec(x)+1)/(tan(x))=(sin(x))/(1-cos(x))



    2. Relevant equations

    Trig Identities



    3. The attempt at a solution

    I decided to try and prove the identity by manipulating the function on the right side.

    I multiplied both the numerator and denominator by (1+cos) and got
    (sin(x)(1+cos))/(1-cos^2)
    →(sin(x)(1+cos))/(sin^2)
    →(1+cos)/(sin)
    →(csc)+(1/tan)

    I'm stuck after this point.
    All help is much appreciated.
    Thank you.
     
  2. jcsd
  3. Mar 7, 2012 #2
    Re: (sec(x)+1)/tan(x)=(sin(x))/(1-cos(x))

    You're so close...

    You have (1+cos)/(sin)

    divide numerator and denominator by cos...
     
  4. Mar 7, 2012 #3
    Re: (sec(x)+1)/tan(x)=(sin(x))/(1-cos(x))


    Thank you very much!

    I would never have thought of multiplying by (1/cos) because it seemed so...random, yet it works.

    Do you have any tips on how to see things like that?
     
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