Description
How to change cos4x into 2cos^2 2x-1?
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Explanation & Answer
cos4x
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
Hence
cos4x = 2cos^2 2x - 1
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