- #1
stfz
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Homework Statement
Prove that: ##sin x + sin 2x + cos x + cos 2x = 2\sqrt{2} cos (\frac{x}{2}) sin(\frac{3x}{2}+\frac{\pi}{4})##
Homework Equations
We know all the double, compound, and half angle formulas.
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
Is equal to the + graph in some intervals, and equal to the - graph in other intervals.
Please help! :)
Thanks
Stephen