题目

cos^6pai/8-sin^6pai/8

提问时间：2021-12-27

答案

cos^6 (π/8)-sin^6(π/8)=(cos^2 (π/8)-sin^2(π/8)) *(cos^4 (π/8) + cos^2 (π/8)sin^2(π/8)+sin^4(π/8)) =cosπ/4 * ((cos^2 (π/8) + sin^2(π/8))^2 - cos^2 (π/8)sin^2(π/8))
= √2/2 * (1 - 1/4 * sin^2(π/4))
=√2/2 * (1 - 1/8)
=7√2/16.