分类：教育/科学-理工学科-数学
问题：一道数学题计算:cosπ/17*cos2π/17*cos4π/1 
计算:cπ/17*cos2π/17*cos4π/17*cos8π/17=
回答：cos(π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=[1/2sin(π/17)][2sin(π/17)cos(π/17)]cos(2π/17)cos(4π/17)cos(8π/17)
=1/[2sin(π/17)]sin(2π/17)cos(2π/17)cos(4π/17)cos(8π/17)
=[1/4sin(π/17)]sin(4π/17)cos(4π/17)cos(8π/17)
=[1/8sin(π/17)sin(8π/17)cos(8π/17)
=[1/16sin(π/17)]sin(16π/17)
=(1/16)[sin(16π/17)/sin(π/17)]
=(1/16)[sin(π/17)/sin(π/17)]
=1/16.