Question

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

Answer 1

Answer:

Step-by-step explanation:

LHS = 2sec2A − sec4A − 2cosec2A + cosec4A       = sec2A[2 − sec2A] − cosec2A[2 − cosec2A]       = (1+tan2A)[2−(1+tan2A)] − (1+cot2A)[2− (1+cot2A)]       = (1+tan2A)(2−1−tan2A) − (1+cot2A)(2−1−cot2A)       = (1+tan2A)(1−tan2A) − (1+cot2A)(1−cot2A)       = [(1)2 − (tan2A)2] −  [(1)2 − (cot2A)2]       = (1 − tan4A) − (1 − cot4A)       = 1 − tan4A − 1 + cot4A       = cot4A − tan4ARHS =cot4A − tan4AHence, LHS = RHS