2/3+siny-cos^2x=sin^2x+siny-1/3
=sin^2x-sinx+2/3-1/3
=sin^2x-sinx+1/3
=(sinx-1/2)^2+1/12,
因为-1<=siny<=1,则-1/3<=sinx<=1,
设sinx=z,-1/3<z<=1
f(z)=(z-1/2)^2+1/12>=1/12
当,-1/3<=z<1/2,f(z)为减函数f(z)<=f(-1/3)=7/9
当1/2<=z<=1,f(z)为增函数,f(z)<=f(1)=1/3
所以2/3+siny-cos^2x的取值范围为[1/12,7/9]
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