求函数f(x)=2sin(π 3-x)-cos(π 6 x)

∵f（x）＝cos（2x－π/3）＋（sinx）^2－（cosx）^2＝cos（2x－π/3）－cos2x＝2sin（2x－π/6）sin（π/6）＝sin（2x－π/6）.∴g（x）＝［sin（2x

y=sinx的对称轴方程x=πk+π/23x+(2π)/5＝πk+π/23x=πk+π/10x=πk/3+π/30,k∈Z

1、由于函数g(x)=sin(2(x－a)+π/3)为偶函数,所以g(x)的图像关于y轴对称,即函数g(x)当x=0时取得最值,所以g(0)=±1,解得sin(π/3－2a)=±1,sin(2a－π/

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

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

因为f(x)=根号3sin(2x-π/6)+2sin的平方（x-π/12)=根号3sin(2x-π/6)-（1-2sin的平方（x-π/12)）+1=根号3sin(2x-π/6)-cos(2x-π/6

f(x)=2sin(x/4)cos(x/4)-2√3sin²(x/4)+√3=sin(x/2)+√3cos(x/2)=2sin(x/2+π/3)最小正周期T=2π/(1/2)=4π祝你开心!

f(x)=cos(x-π|3)-sin(π|2-x)=1/2cosx+√3/2sinx-cosx=-1/2cosx+√3/2sinx=-cos(x+π/3)对定义域内的每一个x,当x增加到2π时,函数

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

f(x)=[2sin(x+π/3)+sinx]cosx-根号3sin^2x和差角公式展开f(x)=(sinx+根号3cosx+sinx)cosx-根号3sin2x=2sinx*cosx+根号3cosx

f(x)=2cosx*(1/2*sinx+√3/2*cosx)-√3sin²x+sinxcosx=sinxcosx+√3*cos²x-√3sin²x+sinxcosx=2

因为3>0,所以要使函数f(x)=3sin(-2x+π/4）为减则有π/2+2kπ

1.f(x)=2cosx*sin(x+π/3)-√3﹙sinx﹚^2+sinx*cosx=2cosx*﹙sinxcosπ/3+cosxsinπ/3﹚-√3﹙sinx﹚^2+sinx*cosx=cosx

sin(2x+π/3)=±12x+π/3=kπ+π/2所以对称轴是x=kπ/2+π/12sin(2x+π/3)=02x+π/3=kπx=kπ/2-π/6所以对称中心是(kπ/2-π/6,0)sin递增

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

[-5π/12+kπ,π/12+kπ]

sin(x+π/4)=sin(x-π/4+π/2)=cos(x-π/4)所以原式=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)=cos(2x-π/3)+sin(2x-π/2)=1

（Ⅰ）最小正周期T＝2π2＝π…（3分）当sin(2x−π3)＝1时，f（x）max=1+2=3…（6分）（Ⅱ）由−π2+2kπ≤2x−π3≤π2+2kπ，k∈Z…（9分）得−π12+kπ≤x≤5π1

因为2x+π/3=kπ,k∈Z,所以x=1/2kπ-π/6,k∈Z,所以函数y=sin(2x+π/3)的图象的对称中心：（1/2kπ-π/6,0）k∈Z．因为2x+π/3=kπ+π/2k∈Z,所以x=