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
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![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](/uploads/image/z/2615435-35-5.jpg?t=cos%CF%80%2F11%2Acos2%CF%80%2F11%2Acos3%CF%80%2F11%2Acos4%CF%80%2F11%2Acos5%CF%80%2F11%E4%B8%8A%E5%BC%8F%E4%B8%BA%E4%BD%95%E7%AD%89%E4%BA%8Ecos%CF%80%2F11%2Acos2%CF%80%2F11%2Acos4%CF%80%2F11%2Acos8%CF%80%2F11%2Acos16%CF%80%2F11)
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
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
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
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
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