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Expressed purely in terms of cos(alpha), what does cos(4*alpha) equal?

1. 8*cos⁴(alpha) - 8*cos²(alpha) + 1
2. 8*cos⁴(alpha) + 8*cos²(alpha) - 1
3. 4*cos⁴(alpha) - 4*cos²(alpha) + 1
4. 8*cos⁴(alpha) - 8*cos²(alpha) - 1

Correct answer: 8*cos⁴(alpha) - 8*cos²(alpha) + 1

Solution

Using cos(4a) = 2*cos²(2a) - 1 with cos(2a) = 2*cos²(a) - 1 gives cos(4a) = 8*cos⁴(a) - 8*cos²(a) + 1.

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