cos^6 (π⼀8)-sin^6(π⼀8)=?

cos^6 (π/8)-sin^6(π/8)
=(cos^2 (π/8))^3-(sin^2(π/8))^3
=(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^4 (π/8)-cos^2 (π/8)*sin^2(π/8)+sin^4(π/键橡8))
=(cosπ/陵辩4)(((cos^2 (π/8)+sin^2(π/8))^2-3cos^2 (π/8)*sin^2(π/8))
=(cosπ/4)(1-3cos^2 (π/8)*sin^2(π/8))
=(cosπ/4)(1-3/4*sin^2(π/尺亮缺4))
=....

7√2/16.

cos^6 (π/8)-sin^6(π/租悔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))
= √拿型尺消高2/2 * (1 - 1/4 * sin^2(π/4))
=√2/2 * (1 - 1/8)
=7√2/16.

(7√2)/16