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!

Trig proof help!

  1. Oct 29, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove that: ##sin x + sin 2x + cos x + cos 2x = 2\sqrt{2} cos (\frac{x}{2}) sin(\frac{3x}{2}+\frac{\pi}{4})##

    2. Relevant equations
    We know all the double, compound, and half angle formulas.

    3. The attempt at a solution
    Taking on the RHS, we have
    Expanding with half angle formula and compound angle formula
    Hence we can cancel the sqrt(2) on the left, and replace sin/cos (pi/4) with exact values
    And we have
    If we expand the half angles in the right bracket
    And then the sqrt(2) on the bottom can multiply to make 2, we can +/- them together
    And cancel the twos.
    Is it possible to cancel the +/- signs?
    However, the graph of my result does not match that of the original.
    For example, if I graph
    As two graphs, one with a + and the other with a -, I find that the original graph upload_2014-10-30_9-39-43.png
    Is equal to the + graph in some intervals, and equal to the - graph in other intervals.

    Please help! :)

  2. jcsd
  3. Oct 29, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Have you ever seen this formula? ##Asin(x) + Bcos(x) = \sqrt{A^2+B^2}sin(x+α) \ \ (α = tan^{-1}(\frac{B}{A}))##
  4. Oct 29, 2014 #3
    Hmm... Maybe that will work! Thanks for the suggestion, I will try it
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Trig proof help!
  1. Help with trig proof (Replies: 8)

  2. Trig proof (Replies: 8)

  3. Trig proof (Replies: 5)

  4. Trig Proof (Replies: 4)