f(x)=(1/2)(sinx+cos)-(1/2)|sinx-cosx|的值域
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f(x)=(1/2)(sinx+cosx)-(1/2)|sinx-cosx|
=(√2/2)sin(x+π/4)-(√2/2)|sin(x-π/4)|
=(√2/2)cos(x-π/4)-(√2/2)|sin(x-π/4)|
=(√2/2)[cos(x-π/4)-|sin(x-π/4)|]
cos(x-π/4)=1 sin(x-π/4)=0时，f(x)有最大值f(x)max=√2/2
cos(x-π/4)=-√2/2 sin(x-π/4)=√2/2时，f(x)有最小值f(x)min=-1
综上，得函数的值域为[-1，√2/2]
=(√2/2)sin(x+π/4)-(√2/2)|sin(x-π/4)|
=(√2/2)cos(x-π/4)-(√2/2)|sin(x-π/4)|
=(√2/2)[cos(x-π/4)-|sin(x-π/4)|]
cos(x-π/4)=1 sin(x-π/4)=0时，f(x)有最大值f(x)max=√2/2
cos(x-π/4)=-√2/2 sin(x-π/4)=√2/2时，f(x)有最小值f(x)min=-1
综上，得函数的值域为[-1，√2/2]
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