Final answer:
To prove the equation 2cos²(2x)-1 = cos4x, we can use the double angle identity for cosine.
Step-by-step explanation:
To show that 2cos²(2x)-1 = cos4x, we need to use a trigonometric identity. The double angle identity for cosine states that cos(2θ) = 2cos²(θ) - 1. We can use this identity to rewrite the equation as cos(4x) = cos(2(2x)). Since cosine is an even function, it holds that cos(θ) = cos(-θ). Therefore, cos(4x) = cos(-4x) and this implies that 4x = -4x. Hence, we have proved that 2cos²(2x)-1 = cos4x.
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