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Consider the trigonometric identity (1 - tan A)/(1 + tan A) = (cot A - 1)/(cot A + 1). Is this identity valid for all admissible A?

1. True for all admissible A
2. False, it never holds
3. True only when A = 45 deg
4. True only when A = 0 deg

Correct answer: True for all admissible A

Solution

Substituting cot A = 1/tan A and multiplying through by tan A makes the right side identical to the left, so it is an identity.

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