1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook