已知函数y=(sinx)^4+2√3sinxcosx-(cosx)^4
问题描述：
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
答
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﹚,...