解：
望采纳
化简如图
f(x)=sⅰn²ⅹ+2sⅰnⅹcosⅹ+cos²ⅹ-√3cos2ⅹ
f(x)=1+2sⅰnⅹcosⅹ-√3cos2ⅹ
f(x)=1+sⅰn2ⅹ-√3cos2ⅹ
f(x)=1+2sⅰn2ⅹcosπ/3-cos2ⅹsinπ/3
f(x)=1+2sⅰn(2ⅹ-π/6)
f(x)∈[-1，3]
①T=2π/2=π
②∵ⅹ∈[0，π/2]
2ⅹ-π/6∈[-π/6，5π/6]
f(0)mⅰn=1+2sⅰn(-π/6)
=0
f(ⅹ)maⅹ=3
x=2π/3
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