How to change cos4x into 2cos^2 2x-1?
cos(2x + 2x)
cos2xcos2x - sin2xsin2x
cos^2 2x - sin^2 2x
As sin^2 2x = 1 - cox^2 2x, So
cos^2 2x - (1 - cos^2 2x)
cos^2 2x - 1 + cos^2 2x
cos^2 2x + cos^2 2x - 1
2cos^2 2x - 1
cos4x = 2cos^2 2x - 1
How do you get sin^2 2x = 1 - cos^2 2x?
Because its one of the basic identity. which is
sin^2 x + cos^2 x = 1
So in the question, there is 2x in the angle, so we put 2x
sin^2 2x + cos^2 2x = 1
Now solving for sin^2 2x, we get
sin^2 2x = 1 - cos^2 2x
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