y=sin(x+π/6)+sin(x-π/6)+cosx ,x∈[-π/2,π/2]的值域

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y=sin(x+π/6)+sin(x-π/6)+cosx ,x∈[-π/2,π/2]的值域
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y=sin(x+π/6)+sin(x-π/6)+cosx ,x∈[-π/2,π/2]的值域
y=sin(x+π/6)+sin(x-π/6)+cosx ,x∈[-π/2,π/2]的值域

y=sin(x+π/6)+sin(x-π/6)+cosx ,x∈[-π/2,π/2]的值域
y=sinxcosπ/6+cosxsinπ/6+sinxcosπ/6-cosxsinπ/6+cosx
=√3sinx+cosx
=2(sinx√3/2+cosx*1/2)
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
-π/3

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