Question

2 sec^2A- sec^4 A - 2 cosec^2 A + cosec^4 A = cot^4 A - tan^4A​

Answer 1

Answer:

proved

Step-by-step explanation:

2 sec²A - sec⁴A - 2cosec²A + cosec⁴A

= 2 sec²A - 2cosec²A - sec⁴A + cosec⁴A

= 2(sec²A - cosec²A) -[(sec²A)² - (cosec²A)²]

=2(sec²A-cosec²A)+[(sec²A-cosec²A)(sec²A+cosec²A)]

= (sec²A - cosec²A) [2 - (sec²A + cosec²A)]

= (sec²A - cosec²A) (2 - sec²A - cosec²A)

= (sec²A - cosec²A) (1 - sec²A + 1 - cosec²A)

= (sec²A - cosec²A) (tan²A - cot²A)

= (1 - tan²A - 1 - cot²A) (tan²A - cot²A)

= - (tan²A + cot²A) (tan²A - cot²A)

= - (tan⁴A + cot⁴A)

= cot⁴A - tan⁴A

hope it maY help u

= RHS

.Proved