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An elusive trig proof I can't seem to get

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove that:

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

    2. Relevant equations

    There are just trig identities that we can use.

    3. The attempt at a solution
    I've attempted every possible way I can think of and it would just look like jibberish here.
    Last edited: Jul 21, 2011
  2. jcsd
  3. Jul 21, 2011 #2


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    Science Advisor

    What you wrote, sin(x)+ tan(x)/cos(x)+ 1= tan(x). isn't true! For example, if x= 0, then sin(x)= sin(0)= 0, tan(x)/cos(x)= tan(0)/cos(0)= 0/1= 0 so the left side is 1. But the right side, tan(x)= tan(0), is 0.

    What I think you meant was (sin(x)+ tan(x))/(cos(x)+ 1)= tan(x).

    If you multiply both sides of the equation by cos(x) you get
    (sin(x)cos(x)+ sin(x))/(cos(x)+ 1)= sin(x).
  4. Jul 21, 2011 #3
    Sorry yeah, that's what I meant, my mistake. I'll change that right now.
  5. Jul 22, 2011 #4
    Use the fact that tan(x)=sin(x)/cos(x). The proof should just involve two lines of algebra.
  6. Jul 23, 2011 #5
    factor out tan(x) from numerator and u get cos(x)+1 which cancels with denominator
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