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For an acute angle A, the expression (sec 2A + 1)*sqrt(sec² A - 1) simplifies to which of the following?

1. tan 2A
2. tan A
3. sin 2A
4. sec 2A

Correct answer: tan 2A

Solution

Since sqrt(sec² A - 1) = tan A and (sec 2A + 1) = 2 cos² A/cos 2A, the product becomes 2 sin A cos A/cos 2A = sin 2A/cos 2A = tan 2A.

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