Question

Prove that: cos⁴A+Sin⁴A=1/4(3+Cos4A)​

Answer 1

Step-by-step explanation:

prove 2 sin^2 A + cos^4 A = 1 + sin^4 A?

LHS = 2 sin^2A + cos^4 A

= 2 sin^2 A + (cos^2 A)^2

= 2 sin^2 A + (1 - sin^2 A)^2

= 2 sin^2 A + 1 - 2sin^2 A + sin^4A

= 1 + sin^4 A

= RHS.

Proved.