sinx*(-1)=3/2*cosx
tanx=-3/2
2cos²x-sin2x
=1+cox2x-sin2x
=1+[1-tan²x]/[1+tan²x]-2tanx]/[1+tan²x]
=1+[1-tan²x-2tanx]/[1+tan²x]
=1+[1-9/4+3]/[1+9/4]
=1+[4-9/4]/[1+9/4]
=1+[7/4]/[13/4]
=1+7/13
=20/13a+b=(sinx+cosx,-1/2),
f(x)=(a+b)*b=(sinx+cosx)cosx+1/2
=(1/2)[sin2x+cos2x+2]
=(√2）sin(2x+π/4)+1,
x∈[-π/2,0],则（2x+π/4)∈[-3π/4,π/4],
sin(2x+π/4)∈[-1,(√2）/2],
∴f(x)|max=2.