Question

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

Answer 1

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`