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Proving trigonometric equations

  1. Oct 19, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi there, I am attempting to prove a trigonometric equation using the half angle and double angle formulae

    2. Relevant equations
    See image one...

    3. The attempt at a solution
    See image two...

    I get stuck after the second line and can't see how to continue, please help.
     

    Attached Files:

  2. jcsd
  3. Oct 19, 2014 #2
    Your denominator is a difference of squares, and can be factored...
     
    Last edited: Oct 19, 2014
  4. Oct 20, 2014 #3
    1 / cosA + sin2A / cos2A = (1+sin2A) / cos2A . And you've got to change 1 = (sinx)^2 + (cosx)^2.

    Then, 1+sin2A = (sinA) ^2 + (cosA)^2 + sin2A = (sinA)^2 + 2sinAcosA + (cosA)^2 = (sinA+ cosA)^2

    and cos2A = (cosA)^2 - (sinA)^2 =(cosA-sinA)(cosA+sinA)

    so (1+sin2A) / cos2A = (sinA + cosA) ^2 / (cosA-sinA)(cosA+sinA) = (sinA + cosA ) / (cosA - sinA)
     
  5. Oct 20, 2014 #4
    This is hard for me to understand, but I'm pretty sure this is incorrect, I believe you made an error copying the problem:
    The actual problem was:
    [itex] \frac{1}{\cos(2x)} + \frac{\sin(2x)}{\cos(2x)} [/itex]
    While you wrote:
    [itex] \frac{1}{\cos(x)} + \frac{\sin(2x)}{\cos(2x)} [/itex]
    As with most problems, I'm sure there are multiple ways to do it, but this is not very close to what I got when I did this problem, but it may just be because I am having a hard time reading your solution
     
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