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The expression sec⁴ A - sec² A is identically equal to which of the following?

1. tan⁴ A + tan² A
2. tan⁴ A - tan² A
3. sec⁴ A + sec² A
4. tan² A - tan⁴ A

Correct answer: tan⁴ A + tan² A

Solution

Factoring gives sec² A (sec² A - 1) = sec² A * tan² A, and replacing sec² A with 1 + tan² A yields tan⁴ A + tan² A.

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