作业帮cos^2 π/8+cos ^2 3π/8+ cos^2 5π/8+cos^2 7π/8=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 03:01:56
cos^2 π/8+cos ^2 3π/8+ cos^2 5π/8+cos^2 7π/8=?
cos^2 π/8+cos ^2 3π/8+ cos^2 5π/8+cos^2 7π/8=?
cos^2 π/8+cos ^2 3π/8+ cos^2 5π/8+cos^2 7π/8=?
不同那些公式,太麻烦了
因为cos(π-α)=-cos α
所以cos 7π/8= -cos π/8
cos^2 7π/8=cos^2 π/8
同理cos^2 5π/8=cos^2 3π/8
原式=2（cos^2 π/8+cos^2 3π/8）
这里用到cos(π/2-α)=sin α
显然cos^2 π/8=sin^2 3π/8
原式=2（sin^2 3π/8+cos^2 3π/8）
=2
cos²(π/8)+ cos²(3π/8)+ cos²(5π/8)+ cos²(7π/8)
=[1+cos(π/4)]/2+[1+cos(3π/4)]/2+[1+cos(5π/4)]/2+[1+cos(7π/4)]/2
=2+[cos(π/4)+ cos(3π/4)+ cos(5π/4)+ cos(7π/4)]/2
=2
cos^2 π/8+cos ^2 3π/8+ cos^2 5π/8+cos^2 7π/8=?
cos(π/17)*cos(2π/17)*cos(4π/17)*cos(8π/17)
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