Which expression is equivalent to cosine of 4 x ?

Use the double-angle identity cos(2θ) = 2 cos²(θ) − 1. Applying it with θ = 2x gives cos(4x) = 2 cos²(2x) − 1. Since cos(2x) = 2 cos²(x) − 1, substituting gives 2(2 cos² x − 1)² − 1, which is choice A.

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