Question

i will mark u the brainliest pls answer this question​

Answer 1

Step-by-step explanation:

I will take (A) instead of theta (theta is absent in keyboard)

2/cos^2A - 1/cos^4A - 2/sin^2A + 1/sin^4A = cot^4A - tan^4A

we know that

1/cosA = secA

1/sinA = cosecA

so change it

2sec^2A - sec^4A - 2cosec^2A + cosec^4A

2sec^2A - (sec^2A)^2 - 2cosec^2A + (cosec^2A)^2

now by formulas

sec^2A = 1+tan^2A

cosec^2A = 1+cot^2A

so again change it

2(1+tan^2A) - (1+tan^2A)^2 - 2(1+cot^2A) + (1+cot^2A)^2

2 + 2tan^2A - (1 + tan^4A + 2tan^2A) - 2 -2cot^2A + (1 + cot^4A + 2cot^2A)

2 + 2tan^2A - 1 - tan^4A - 2tan^2A - 2 - 2cot^2A +1 + cot^4A + 2cot^2A

now at this moment some of the terms are cancelling out

remaining is

cot^4A - tan^4A

hence proved