Let the function y = (1 − cos x)^(−1), where x ≠ 2nπ and n is an integer. What is ∫ y dx equal to?
A.−tan(x/2) + c
B.−cot(x/2) + c✓ Correct
C.tan(x/2) + c
D.cot(x/2) + c
Explanation
Using 1 − cos x = 2 sin²(x/2), we get y = 1/(2 sin²(x/2)) = (1/2) cosec²(x/2). Then ∫ y dx = (1/2) ∫ cosec²(x/2) dx = (1/2)·(−2 cot(x/2)) + c = −cot(x/2) + c.
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