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Math Trig Identities?

  1. Dec 6, 2012 #1
    Hi im in need of some help for this question:

    1+tanx/1-tanx = tan(x+(∏/4))

    It is easy to solve with the tan trig identites on the right side however, my teacher had told me to do it with SIN and COS only. Im not sure if its possible and was looking for some insight

    Left Side:

    Right Side:
    End up with
    {(SinxCos∏/4) + (CosxSin∏/4)}/ (CosxCos∏/4) - (SinxSin∏/4)

    Can anyone give me some insight?
  2. jcsd
  3. Dec 6, 2012 #2


    User Avatar
    Homework Helper

    A good first step is to replace cos([itex]\pi[/itex]/4) and sin([itex]\pi[/itex]/4) by their actual values.
  4. Dec 6, 2012 #3
    Yes. I have tried that but then i get stuck at:

    (Sinx(√2/2)) + (Cosx(√2/2)) / (Cosx(√2/2)) - (Sinx(√2/2))

    IS there anything i can do?
  5. Dec 6, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    Don't get confused by all the notation. This is just the same as simplfying something like
    $$\frac{3a + 3b}{3c - 3d}$$
  6. Dec 6, 2012 #5
    I dont think im catching it. I understand how to simplify the example you had but i cannot factor out a sin or a cos?
  7. Dec 6, 2012 #6
    Nevermind, I feel reallydumb... i got it, thanks guys
  8. Dec 6, 2012 #7


    Staff: Mentor

    The left side needs parentheses!

    What you wrote is 1 + (tanx)/1 - tanx, which is equal to 1.

    What you meant was (1 + tanx)/(1 - tanx).
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