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If tan(theta) + cot(theta) = 2, find the value of sin(theta).

1. 1/sqrt(2)
2. sqrt(3)/2
3. 1/2
4. 1

Correct answer: 1/sqrt(2)

Solution

tan theta + cot theta = 1/(sin theta cos theta) = 2 means sin theta cos theta = 1/2, i.e. sin 2theta = 1, so theta = 45 deg and sin theta = 1/sqrt(2).

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