Question

sec^4A-cos^4A=1-2cos^2A

Answer 1

LHS = sin⁴A - cos⁴A
= (sin²A - cos²A)(sin²A + cos²A)

As you know, sin²x + cos²x = 1
So, sin²A + cos²A = 1

∴ LHS = (sin²A - cos²A) × 1
= (1 - cos²A - cos²A) [ sin²x = 1 - cos²x from identities ]
= 1 - 2cos²A = RHS
[Hence, proved]