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Prove the identity tan A/(1 - cot A) + cot A/(1 - tan A) = sec A * cosec A + 1. Which statement correctly identifies this identity?

1. It is a valid identity equal to 1 + sec A * cosec A
2. It is a valid identity equal to 1 - sec A * cosec A
3. It is a valid identity equal to sec A * cosec A only
4. It is not an identity (false for some A)

Correct answer: It is a valid identity equal to 1 + sec A * cosec A

Solution

Substituting tan A and cot A in terms of sin and cos and simplifying yields exactly 1 + sec A * cosec A, confirming the identity.

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