因为coskx=f(cosx)f(sinx)=f[cos(-π/2+x)]=cos(-kπ/2+kx)又因为k是4的倍数加1的自然数即k=4t+1 (t为非负整数)所以f(sinx)=cos(-kπ/2+kx)=cos(-2tπ-π/2+kx =cos(-π/2+kx)=sinkx得证
