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Is the identity cot A = (1/2)(cot(A/2) - tan(A/2)) correct?

1. True
2. False
3. True only for A in (0, pi/2)
4. Cannot be determined

Correct answer: True

Solution

The difference equals cos A / ((1/2) sin A) = 2 cot A, so half of it is cot A.

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