求值:cosπ⼀7*cos2π⼀7*cos3π⼀7

2024-12-25 11:15:45
推荐回答(1个)
回答1:

解答:
cosπ/7*cos2π/7*cos3π/7

=-cosπ/7*cos2π/7*cos4π/7
=-sin(π/7)*cos(π/7)*cos(2π/7)*cos(4π/7)/sin(π/7)
=-(1/2)sin(2π/7)*cos(2π/7)*cos(4π/7)/sin(π/7)
=-(1/4)sin(4π/7)*cos(4π/7)/sin(π/7)

=-(1/8)cos(8π/7)/sin(π/7)
因为 sin(8π/7)=sin(π+π/7)=-sin(π/7)
=1/8