sin kπ/4(k从1到n)的和为什么等于{cos[π/8]-cos[(n+1/2)π/4]}/2sin(π/8)?
问题描述:
sin kπ/4(k从1到n)的和为什么等于{cos[π/8]-cos[(n+1/2)π/4]}/2sin(π/8)?
答
sin(nπ/4)=[2sin(nπ/4)sin(π/8)]/[2sin(π/8)],然后对[2sin(nπ/4)sin(π/8)]用积化和差,2sin(nπ/4)sin(π/8)=cos(nπ/4-π/8)-cos(nπ/4+π/8)=cos[(n-1)π/4+π/8]-cos(nπ/4+π/8)所以sin(nπ/4)=[cos[(n-1)...