sin(派/8)^4-cos(派/8)^4的值是
问题描述：
sin(派/8)^4-cos(派/8)^4的值是
答
[sin(π/8)]^4-[cos(π/8)]^4
={[sin(π/8)]^2-[cos(π/8)]^2}*{[sin(π/8)]^2+[cos(π/8)]^2}
=[sin(π/8)]^2-[cos(π/8)]^2 * 1
=-cos[2*π/8]=-cos[π/4]
=-√2/2
答
sin(π/8)^4-cos(π/8)^4
=[sin(π/8)^2-cos(π/8)^2][sin(π/8)^2+cos(π/8)^2]
=sin(π/8)^2-cos(π/8)^2
=-[cos(π/8)^2-sin(π/8)^2]
=-cos(2*π/8)
=-cos(π/4)
=-√2/2