证明cos【(4n+1)π/4+x】-cos[(4n-1)π/4-x]=0(n属于z)

问题描述:

证明cos【(4n+1)π/4+x】-cos[(4n-1)π/4-x]=0(n属于z)

n=2k
cos【(4n+1)π/4+x】-cos[(4n-1)π/4-x]=cos【π/4+x】-cos[π/4+x]=0
n=2k+1
cos【(4n+1)π/4+x】-cos[(4n-1)π/4-x]=-cos【π/4+x】+cos(π/4+x)=0