Question

cosec⁴a-2cosec²a+2sec²a-sec⁴a=cot⁴a-tan⁴a
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Answer 1

Answer:

2sec2 A - sec4 A - 2cosec2 A + cosec4 A Using sec2 A = tan2 A + 1 and cosec2 A = cot2 A + 1, we have = 2(tan2 A + 1) - (tan2 A + 1)2 - 2(cot2 A + 1) + (cot2 A + 1)2 = 2tan2 A + 2 - tan4 A - 1 -2tan2 A - 2cot2 A - 2 + cot4 A + 1 + 2cot2 A = cot4 A - tan4 A = RHS = Hence proved

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