大师作文网cos(π÷5）＋cos(2π÷5)等于多少?不要用计算器!
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/12 05:46:16
cos(π÷5）＋cos(2π÷5)等于多少?不要用计算器!
cos(π/5)-cos(2π/5)
=cos(π/5)+cos(3π/5)
=cos(2π/5-π/5)+cos(2π/5+π/5)
=cos(2π/5)*cos(π/5)+sin(2π/5)*sin(π/5)+cos(2π/5)*cos(π/5)-sin(2π/5)*sin(π/5)
=2cos(2π/5)*cos(π/5)
=2sin(π/10)*cos(π/5)
=2sin(π/10)*[cos(π/10)/cos(π/10)]*cos(π/5)
=[sin(π/5)/cos(π/10)]*cos(π/5)
=[sin(π/5)*cos(π/5)]/cos(π/10)
=(1/2)sin(2π/5)/cos(π/10)
=(1/2)cos(π/10)/cos(π/10)
=1/2
=cos(π/5)+cos(3π/5)
=cos(2π/5-π/5)+cos(2π/5+π/5)
=cos(2π/5)*cos(π/5)+sin(2π/5)*sin(π/5)+cos(2π/5)*cos(π/5)-sin(2π/5)*sin(π/5)
=2cos(2π/5)*cos(π/5)
=2sin(π/10)*cos(π/5)
=2sin(π/10)*[cos(π/10)/cos(π/10)]*cos(π/5)
=[sin(π/5)/cos(π/10)]*cos(π/5)
=[sin(π/5)*cos(π/5)]/cos(π/10)
=(1/2)sin(2π/5)/cos(π/10)
=(1/2)cos(π/10)/cos(π/10)
=1/2