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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
    upload_2014-10-30_9-39-43.png
    Expanding with half angle formula and compound angle formula
    upload_2014-10-30_9-39-43.png
    Hence we can cancel the sqrt(2) on the left, and replace sin/cos (pi/4) with exact values
    And we have
    upload_2014-10-30_9-42-59.png
    If we expand the half angles in the right bracket
    upload_2014-10-30_9-46-11.png
    And then the sqrt(2) on the bottom can multiply to make 2, we can +/- them together
    upload_2014-10-30_9-48-2.png
    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
    upload_2014-10-30_9-40-54.png
    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! :)
    Thanks

    Stephen
     
  2. jcsd
  3. Oct 29, 2014 #2

    PeroK

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    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
     
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