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Prove that cot(pi/4 + theta) * cot(pi/4 - theta) = 1. Which statement is correct?

1. True for all theta where both cotangents are defined
2. True only when theta = 0
3. Equals tan²(theta), not 1
4. False for all theta

Correct answer: True for all theta where both cotangents are defined

Solution

The two angles are complementary (sum pi/2), so cot(pi/4+theta) = tan(pi/4-theta); multiplying by cot(pi/4-theta) gives tan*cot = 1.

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