You began the problem correctly. Continue to use the cos "double angle" formula, applying it twice.
cos4x = cos[2(2x)] = 2 cos^2(2x) - 1
= 2(2cos^2 x - 1)^2 -1
= 2*[4 cos^4 x -4cos^2 x +1) -1
= 8cos^2 x -8cos^2 x +1
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