cos(π÷5)+cos(2π÷5)等于多少?不要用计算器!

来源:学生作业帮助网 编辑:作业帮 时间:2024/06/02 02:40:12
cos(π÷5)+cos(2π÷5)等于多少?不要用计算器!
x)K/8px=tF`Ov=]2醉OvX|ʊ>_76IEh/P@&X. bɀU"|ml4&gAL4H*ulM=T T4TG0cѵD-&NB&ID&O: "/.H̳E;R0

cos(π÷5)+cos(2π÷5)等于多少?不要用计算器!
cos(π÷5)+cos(2π÷5)等于多少?不要用计算器!

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