You need to use the double angle formula to re-write the expression, such that:
`cos^2 x - 1/2 = (2cos^2 x - 1)/2 = (cos 2x)/2`
`cos 2x = cos(x+x) = cos x*cos x - sin x*sin x`
`cos 2x = cos^2 x - sin^2 x`
Replacing `1 - cos ^2 x` for `sin^2 x` yields:
`cos 2x = cos^2 x- 1 + cos^2 x`
`cos 2x = 2cos^2 x - 1 `
Hence, using the double angle formula to re-write the expression yields `cos^2 x - 1/2 = (cos 2x)/2`
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