Question

Prove that
(sin^4A+cos^4A)/1-2sin^2Acos^2Q=1

Answer 1

Open the identity (sin²A+cos²A)²

as (a+b)²=a²+b²+2ab

(sin²A+cos²A)²=sin^4A+cos^4A+2sin²Acos²A        use sin²a+cos²a=1

(1)² - 2sin²Acos²A = sin^4A+cos^4A

1-2sin²Acos²A = sin^4A+cos^4A

hence proved

Hope that this answer will help you