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Is the trigonometric identity 1 + cos²(2*theta) = 2*(cos⁴(theta) + sin⁴(theta)) valid for all values of theta?

1. Yes, it is an identity true for all theta
2. No, it holds only when theta = 0
3. No, it holds only when cos(2*theta) = 0
4. No, the two sides differ by sin²(2*theta)

Correct answer: Yes, it is an identity true for all theta

Solution

Both sides simplify to 2 - sin²(2*theta), so the equation is a true identity for every theta.

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