f(x)=根号3sin^2(x 4 π)-cos^2-2 1 根号3

1,f(x)=sin²x+√3sinxcosx+2cos²x＝1－cos²x＋√3/2sin2x+2cos²x＝cos²x＋√3/2sin2x+1=(

f(x)=2cosxsin(x+60°)-√3sin²x+sinxcosx=2cosx(sinxcos60º+cosxsin60º)-√3sin²x+sinxc

f(x)=(sin²x+cos²x)+(√3/2)(2sinxcosx)+cos²x=1+(√3/2)sin2x+(1+cos2x)/2=(√3/2)sin2x+(1/2

f(x)=cos^2x-sin^2x+2(根号3)sinxcosx+1=cos2x+(根号3)sin2x+1=2{(1/2)cos2x+[(根号3)/2]sin2x}+1=2sin(2x+派/6)+1

由题意可得:f(x)=sin(2x+π/3)-√3sin^2x+sinxcosx+√3/2=sin(2x+π/3)-√3(1/2-1/2cos2x)+1/2sin2x+√3/2=2sin(2x+π/3

f(x)=√3(sin^2x-cos^2x)-2sinxcosx=-√3cos2x-sin2x=-2sin(2x+π/3)1.求最小正周期T=π2.设x∈[-π/3,π/3],求函数的值域和单调区间-

f(x)=2sinxcosx+2√3sin²x-√3=2sinxcosx+√3sin²x+√3(sin²x-1)=2sinxcosx+√3sin²x-√3cos

y=sinx^2+根3sinxcosx+2cosx^2=-1/2(1-2sinx^2)+1/2根3*2sinxcosx+2cosx^2-1+3/2=-1/2cos2x+二分之根3倍sin2x+cos2

f(x)=2根号3sin方x+sin2x+根号3＝根号3（2sin方x＋1）＋sin2x＝根号3（1－cos2x＋1）＋sin2x＝2根号3－根号3cos2x＋sin2x＝2sin（2x－60度）＋2

f(x)=2√3sin²x-sin(2x-π/3)=√3-√3cos2x-1/2sin2x+√3/2cos2x=√3-(1/2sin2x+√3/2cos2x)=√3-sin(2x+π/3)T

f(x)=sin2(x+π)+根号3sin(x+π)sin(π-x)-1\2=sin2x－根号3sin²x-1/2=sin2x＋根号3/2cos2x－1=根号7/2sin（2x＋γ）－1co

经济将积极

f(x)=sin^2x+2√3sinxcosx+sin(x+π/4)sin(x-π/4)=(1-cos2x)/2+√3sin2x+(1/2)2sin(x-π/4)cos(x-π/4)=2-2cos2x

（1）f(x)=√3sin(2x+φ)-cos(2x+φ）=2[√3/2*sin(2x+φ)-1/2*cos(2x+φ）]=2sin(2x+φ-π/6)因为是偶函数∴函数f(x)在x=0处取最大值或最

函数f(x)=负根号3sin^2x+sinxcosx应该没^这个符号的吧?如果是没有的话f(x)=负根号3sin2x+sinxcosx=负根号3sin2x+sin2x=(1/2-3^(1/2))sin

（1）化解函数：√3∵f(x)=sin²wx+√3sinwxcoswx+2cos²wx=√3/2sin2wx+sin²wx+cos²wx+cos²wx

f(x)=sin(2x+α)+根号3cos(2x+α)=2sin(2x+α+π/3)∵f(x)图像过（π/12,1)∴f(π/12)=2sin(π/6+π/3+α)=2sin(π/2+α)=2cosα

f(x)=[2sin(x+π/3)+sinx]cosx-√3sin²x=[sinx+√3cosx+sinx]cosx-√3sin²x=2sinxcosx+√3cos²x-

最大值2,最小值－2.通过化简,化成一个三角函数式,即可知道结果.请参考图片.

f(x)=√3sin2x+(1-cos2x)-1=√3sin2x-cos2x=2sin(2x-π/6)最小正周期T=2π/2=π单调增区间：2kπ-π/2=