cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11上式为何等于cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11
问题描述：
cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
上式为何等于cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11
答
cos3π/11=cos(π-8π/11)=-cos8π/11; cos5π/11=-cos(π+5π/11)=-cos16π/11,
所以cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
=cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11 =2sinπ/11*cosπ/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11]/2sinπ/11
=sin2pai/11*cos2π/11*cos4π/11*cos8π/11*cos16π/11]/2sinπ/11
=sin4pai/11*cos4π/11*cos8π/11*cos16π/11]/4sinπ/11
=sin8pai/11*cos8π/11*cos16π/11]/8sinπ/11
=sin16pai/11*cos16π/11]/16sinπ/11=sin32pai/11]/32sinπ/11=sin10pai/11]/32sinπ/11=1/32