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Is the trigonometric identity sin⁸(A) - cos⁸(A) = (sin²(A) - cos²(A))(1 - 2 sin²(A) cos²(A)) true for all A?

1. True
2. False
3. True only for A = 45 deg
4. True only for A in the first quadrant

Correct answer: True

Solution

Factoring the difference of fourth powers and applying the Pythagorean identity reduces the left side exactly to the right side, so it is an identity.

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