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Express 2 sec² A - sec⁴ A - 2 cosec² A + cosec⁴ A in terms of tan A.

1. cot⁴ A - tan⁴ A
2. tan⁴ A - cot⁴ A
3. tan² A - cot² A
4. cot² A - tan² A

Correct answer: cot⁴ A - tan⁴ A

Solution

Writing 2 sec² A - sec⁴ A = 1 - tan⁴ A and cosec⁴ A - 2 cosec² A = cot⁴ A - 1, the sum simplifies to cot⁴ A - tan⁴ A.

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