What is the value of tan A + cot A if tan A = 2?

Question

What is the value of tan A + cot A if tan A = 2?

1. A. 5 2 (Correct answer)
2. B. 3 2
3. C. 1 2
4. D. 7 2

Correct Answer

Option A — 5 2

Detailed Solution & Explanation

The correct answer is 5 2.

Key Points

• tan A + cot A = tan A + 1/tan A. With tan A = 2, this is 2 + 1/2 = 5/2.
• No identities needed here — cot is just the reciprocal of tan, so substitute directly.
• (For the general identity, tan A + cot A = 1/(sin A cos A) = 2/sin 2A, but the reciprocal shortcut is faster when tan A is a clean number.)