cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)=?
请大家帮我解答一下,要过程,谢谢
cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)=?
请大家帮我解答一下,要过程,谢谢
cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)=cos(π/5)+cos(2π/5)-cos(π-3π/5)-cos(π-4π/5)
=cos(π/5)+cos(2π/5)-cos(2π/5)-cos(π/5)=0
cos π=-1 sin π=0
cos a+cos(π-a)=cos a+cos π*cos a-sin π*sin a=cos a-cos a=0
故 cos(π/5)+cos(4π/5)=0 cos(2π/5)+cos(3π/5)=0
cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)=0