求值cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
问题描述：
求值cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
求详细过程和重要步骤的原因(1/4*sin8π/11*cos3π/11*cos5π/11)/2sinπ/11
=(1/4*sin3π/11*cos3π/11*cos5π/11)/2sinπ/11这一步骤是怎么变过来的
答
cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11
=(cosπ/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11*2sinπ/11)/2sinπ/11
=(sin2π/11*cos2π/11*cos3π/11*cos4π/11*cos5π/11)/2sinπ/11
=(1/2*sin4π/11*cos3π/11*cos4π/11*cos5π/11)/2sinπ/11
=(1/4*sin8π/11*cos3π/11*cos5π/11)/2sinπ/11
=(1/4*sin3π/11*cos3π/11*cos5π/11)/2sinπ/11
=(1/8*sin6π/11*cos5π/11)/2sinπ/11
=(1/8*sin5π/11*cos5π/11)/2sinπ/11
=(1/16*sin10π/11)/2sinπ/11
=1/32
解题关键在于利用与构造sin2x=2SinxCosx.如果不明白,等你追问.(1/4*sin8π/11*cos3π/11*cos5π/11)/2sinπ/11得到(1/4*sin3π/11*cos3π/11*cos5π/11)/2sinπ/11的理由是什么？sin(π-x)=sinx