已知向量a=(sinx,3/2),b=(cosx,-1).当a平行于b时,求函数f(x)=(a+b),b在[-派/2,0

(1)(3/2)cosx=-sinx、2sinx=-3cosx、4(sinx)^2=4-4(cosx)^2=9(cosx)^2、(cosx)^2=4/13
2(cosx)^2-sin2x
=2(cosx)^2-2sinxcosx
=2(cosx)^2+3(cosx)^2
=5(cosx)^2
=20/13
(2)a+b=(sinx+cosx,1/2)
f(x)=sinxcosx+(cosx)^2-1/2
=(1/2)sin2x+(1/2)cos2x
=(√2/2)sin(2x+π/4)
-π/2