Linear combination of sin and cos

  • #1
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I have before me that ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)##. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.
 

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  • #2
George Jones
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I have before me that ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)##. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.

It is easy to go from the right to the left by using the standard expansion for ##\cos\left(x+y\right)##.
 

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