How do you use the trig identity $cos2x = cos^2 x - sin^2 x$ to verify that $cos 2x = 2 cos^2 x -1$ ?

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Answer 1 · 2016-01-20T10:52:07

From the identity $sin^2(x) + cos^2(x) = 1$ we can subtract $cos^2(x)$ to obtain $sin^2(x) = 1-cos^2(x)$ . Then,

$cos(2x) = cos^2(x) - sin^2(x)$

$= cos^2(x) - (1 - cos^2(x))$

$= 2cos^2(x) - 1$

How do you use the trig identity cos2x = cos^2 x - sin^2 x cos2x = cos^2 x - sin^2 x to verify that cos 2x = 2 cos^2 x -1cos 2x = 2 cos^2 x -1?