几道高中数学积化和差题

sin[(2n+1)x/2]-sin(x/2)=2cos[(2n+1+1)x/（2*2）]sin[(2n+1-1)x/(2*2)]=右边式子的上部分
（1）cos20。+cos60。+cos100。+cos140。 其中 cos100。+cos140。用和差化积得到为 2cos120。cos20。即-cos20。，后边就自然而然了。
（2）cos(2π/7)+cos(4π/7)+cos(6π/7)
=cos(2π/7)+cos(4π/7)+cos(6π/7)+cos(0)-1
=2cos(3π/7)cos(π/7)+2cos(3π/7)cos(3π/7)-1
=4cos(3π/7)cos(2π/7)cos(π/7)-1
=4cos(4π/7)cos(2π/7)cos(π/7)-1
=4[cos(4π/7)cos(2π/7)cos(π/7)sin(π/7)]/sin(π/7)-1
=2[cos(4π/7)cos(2π/7)sin(2π/7)]/sin(π/7)-1
=[cos(4π/7)sin(4π/7)]/sin(π/7)-1
=1/2sin(8π/7)/sin(π/7)-1
=-1/2