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)

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
【-2,2】.
先用三角函数和差公式展开.
然后用三角函数的统一形式化简,最后得到:
y=2sin(x+π/6)