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Prove the identity (1 + sin 2theta + cos 2theta)/(1 + sin 2theta - cos 2theta) = cot theta.

1. True (both sides equal cot theta)
2. True only for theta = 45 deg
3. Equals tan theta instead
4. Equals 1

Correct answer: True (both sides equal cot theta)

Solution

Substituting the double-angle forms factors the numerator and denominator into 2cos theta(cos theta + sin theta) and 2 sin theta(sin theta + cos theta); the common factor cancels leaving cot theta.

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