Question

Доказать Тождество
COS^4 a-SIN^4 a=1-2 SIN^2 a

Answer 1

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

Answer 2

cos^4a-sin^4a=1-2sin²a
(cos²a)²-sin^4a=1-2sin²a
(1-sin²a)²-sin^4a=1-2sin²a
(1-2sin²a+sin^4a)-sin^4a=1-2sin²a
1+sin^4a-sin^4a=1-2sin²a+2sin²a
1=1