Using the power to double angle formula for cosine, we have:
cos^2(2x) = cos^2(x+x)
= [cos(x)*cos(x)] + [sin(x)*sin(x)] (using the identity cos(a+b) = cos(a)cos(b) – sin(a)sin(b))
= cos^2(x) + sin^2(x)
= 1 (using the identity cos^2(x) + sin^2(x) = 1)
Therefore, cos^2(2x) simplifies to 1 using the power to double angle formula for cosine.
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