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!

Tricky Trig Problem

  1. Sep 3, 2010 #1

    Char. Limit

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    All right, so I was trying to help a friend prove a certain (complicated) trig identity for summer homework, but I got stuck myself... hopefully one of you will be able to help.

    The trig identity in question is...

    [tex]\frac{cos(x)}{1-tan(x)} + \frac{sin(x)}{1-cot(x)} = cos(x) + sin(x)[/tex]

    2. Relevant equations

    3. The attempt at a solution

    So far I've gotten it to...

    [tex]\frac{cos(x)-sin(x)}{sec^2(x)-2tan(x)} - \frac{cos(x)-sin(x)}{csc^2(x)-2cot(x)} = cos(x)+sin(x)[/tex]

    But although I think that's a really nice form (two very similar terms), I have no idea where to go from there. Could one of you help me out?
  2. jcsd
  3. Sep 3, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    I would first express all of the trig functions in terms of sin(x) and cos(x) and then show the two sides are equal. It's pretty straightforward.
  4. Sep 3, 2010 #3


    User Avatar
    Homework Helper

    I would multiply the first fraction by
    [tex]\frac{1 + \tan \,x}{1 + \tan \,x}[/tex]
    and multiply the second fraction by
    [tex]\frac{1 + \cot \,x}{1 + \cot \,x}[/tex].

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Tricky Trig Problem Date
Quadratic discriminant with tricky algebra Jul 18, 2016
A tricky remainder theorem problem Jun 12, 2016
Tricky word problem? Jun 8, 2016
Tricky work problem May 28, 2015
Tricky Trig Simplification, or so I think Feb 20, 2012