The expression ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)## is derived using the cosine addition formula. Specifically, the right-hand side can be expanded using the standard expansion for ##\cos(x+y)##, which confirms the equality. This transformation illustrates the relationship between linear combinations of sine and cosine functions and their representation as a single cosine function with a phase shift.
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Mr Davis 97 said: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.