已知a=(cos(x/2),(根号3)/2-cos(x/2)),b=(（根号3）/2+cos(x/2),sin(x/2)),且a‖b,求【1+（根号2）cos(2x-π/4)】/【sin(x+π/2)】的值
问题描述：
已知a=(cos(x/2),(根号3)/2-cos(x/2)),b=(（根号3）/2+cos(x/2),sin(x/2)),且a‖b,求
【1+（根号2）cos(2x-π/4)】/【sin(x+π/2)】的值
答
∵a‖b∴cos(x/2)sin(x/2)-[√3/2-cos(x/2)][√3/2+cos(x/2)]=0(sinx)/2-3/4+cos^2(x)=0(sinx)/2-3/4+cos^2(x)-1/2+1/2=0(sinx)/2+(cosx)/2=1/4sinx+cosx=1/2[1+√2cos(2x-π/4)]/sin(x+π/2)=[1+√2(cos2xcosπ/4+s...