Question

Cos 4a+sin 4a=1-1/2 sin^2 2a

Answer 1

Answer:

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