∵√(1-sinα)+√(1+sinα)=√3∴[√(1-sinα)+√(1+sinα)]²=(√3)²1-sinα+2√[(1-sinα)(1+sinα)]+1+sinα=32+2√(1-sin²α)=32√(cos²α)=1∵α为第四象限的角∴cosα﹥0∴2√(cos²α...则sin(π/2+α)cos(π/2+α)=多少你好：sin(π/2+α)cos(π/2+α)=sin[2(π/2+α)]/2=[sin(π+2α)]/2=-(sin2α)/2=-sinαcosα∵α是第四象限的角∴sinα﹤0∴sinα=-√(1-cos²α)=-√(1-1/4)=-√(3/4)=-√3/2∴sin(π/2+α)cos(π/2+α)=-(-√3/2)×1/2=√3/4