已知函数y=(sinx)^4+2√3sinxcosx-(cosx)^4若x∈﹙0,π/2﹚,求y的值域若x∈﹙-π/6,π/6﹚,求y的值域

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已知函数y=(sinx)^4+2√3sinxcosx-(cosx)^4若x∈﹙0,π/2﹚,求y的值域若x∈﹙-π/6,π/6﹚,求y的值域
已知函数y=(sinx)^4+2√3sinxcosx-(cosx)^4
若x∈﹙0,π/2﹚,求y的值域
若x∈﹙-π/6,π/6﹚,求y的值域

已知函数y=(sinx)^4+2√3sinxcosx-(cosx)^4若x∈﹙0,π/2﹚,求y的值域若x∈﹙-π/6,π/6﹚,求y的值域
y=(sinx)^4+2√3sinxcosx-(cosx)^4
=(sin^2x+cos^2x)(sin^2x-cos^2x)+√3sin2x
=(sin^2x-cos^2x)+√3sin2x
=√3sin2x-cos2x
=2sin(2x-π/6)
若x∈﹙0,π/2﹚,2x-π/6 ∈﹙-π/6,5π/6)
值域为(-1/2,1]
若x∈﹙-π/6,π/6﹚,2x-π/6 ∈﹙-π/2,π/6)
值域(-1,1/2)

easy