【急】化简f（x）=2cos²x+√3sin2x要求解答问题时要有详细步骤和分析.

【急】化简f（x）=2cos²x+√3sin2x
要求解答问题时要有详细步骤和分析.

f(x)=2(1+cos2x)/2+√3sin2x
=√3sin2x+cos2x+1
=2(sin2x*√3/2+cos2x*1/2)+1
=2(sin2xcosπ/6+cos2xsinπ/6)+1
=2sin(2x+π/6)+1

f(x)=2(1+cos2x)/2+√2sin2x
=√3sin2x+cos2x+1
=2(sin2x*√3/2+cos2x*1/2)+1
=2(sin2xcosπ/6+cos2xπ/6)+1
=2sin(2x+π/6)+1