已知sin（π/2+α）=1/3,则cos(π+2α)的值是?
问题描述：
已知sin（π/2+α）=1/3,则cos(π+2α)的值是?
答
sin（π/2+α）=sin[π/2-(-α)]=cos(-α)=cosα=1/3
则
cos(π+2α)
=cosπcos2α-sinπsin2α
=-cos2α-0=-cos2α
=-(2cos²α-1)
=1-2cos²α
=1-2×(1/3)²
=7/9