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f(x)=a●b=2sinx(cosx+√3sinx)+1-√3
=2sinxcosx+2√3sin²x-√3+1
=sin2x-√3cos2x+1
=2(1/2sin2x-√3/2cos2x)+1
=2sin(2x-π/6)+1
f(x)最小正周期T=π
(2)
∵x∈[0,π/2]
∴2x-π/拿纯亮6∈[-π/6,5π/6]
∴sin(2x-π/6)∈[-1/裤陪2,1]
∴2sin(2x-π/消宽6)∈[-1,2]
∴f(x)的值域为[0,3]
=2sinxcosx+2√3sin²x-√3+1
=sin2x-√3cos2x+1
=2(1/2sin2x-√3/2cos2x)+1
=2sin(2x-π/6)+1
f(x)最小正周期T=π
(2)
∵x∈[0,π/2]
∴2x-π/拿纯亮6∈[-π/6,5π/6]
∴sin(2x-π/6)∈[-1/裤陪2,1]
∴2sin(2x-π/消宽6)∈[-1,2]
∴f(x)的值域为[0,3]
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