Question

Prove that 2 cos² A- cos⁴ A + sin⁴ A= 2​

Answer 1

Step-by-step explanation:

2 cos² A- cos⁴ A + sin⁴ A

2 cos² A+ sin⁴ A - cos⁴ A

2 cos² A + (sin^2 A)^2 - (cos^2 A) ^2

2 cos² A + ( sin^2A + cos^2A) (sin^2A - cos^2A)

2 cos² A + 1×(sin^2A - cos^2A)

2 cos² A + sin^2A - cos^2A

sin^2A + cos^2A

1