快!快!快! 高2数学!

曲线f(x)=cos(2x+φ)(-π<=φ<=0)与直线y=x-m在x=π/6处相切，则f'(π/6)=1，sin(π/3+φ)=-1/2，φ=-π/2 。f(x)=cos(2x-π/2)，曲线f(x)在 x∈[0,π/2] 时（f(x)非负）与x所围成的图形的面积 [0,π/2]∫cos(2x-π/2)dx=[0,π/2]∫d{[sin(2x-π/2)]/2}=1 。