已知函数fx=2cosπ 6x

f(x_=(cosx+sinx)(cosx-sinx)=cos²x-sin²x=cos2x所以T=2π/2=πf(α/2)=cosα=1/3sin²α+cos²

f(x)=cosx-cos(x+π/2)=cosx+sinx=3/4sin^2x+cos^2x+2sinxcosx=9/162sinxcosx=sin2x=9/16-1=-7/16

(1)f（x）=sin（2x+π/6）-cos（2x+π/3）+2cos²x=sin2xcosπ/6+cos2xsinπ/6-[cos2xcosπ/3-sin2xsinπ/3]+2cos&#

若cosα=3/5.α属于(3π/2,2π),sinα=-4/5把f(2α+π/3)代入fx=√2cos(x-π/12),化简原式=cos2α-sin2αcos2α-sin2α怎么化简的就不用我说了吧

令t=sinx则f=(1-t^2)+2t=-t^2+2t+1=-(t-1)^2+2因为|t|

=(1/2)sin2x-(根号3/2)cos2x+(根号3/2)cos2x+(1/2)sin2x+1+cos2x-1=sin2x+cos2x=根号2sin(2x+pi/4)最小正周期为pi-pi/4再

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

f（x）=-sin2x-cos2x+3sin2x-cos2x=2sin2x-2cos2x=2根号2sin(2x-π/4)T=2π/2=π-π/2+2kπ≤2x-π/4≤π/2+2kπk属于Z-π/8+

已知函数fx=sin（2x+π/6）+sin（2x-π/6）+2cos^2x（x属于R）1.求函数fx的最大值及此时自变量函数x的取值集合2.求函数fx的单调递增区间3.求使fx≥2x的x的取值范围(

答：f(x)=2cos²(x/2)-sinx=cosx+1-sinx=-√2*[(√2/2)*sinx-(√2/2)*cosx]+1=-√2*(sinxcosπ/4-cosxsinπ/4)+

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]=cos(2x-π/3)+2sin(x-π/

(1)f(x)=[cos(x-π/6)]^2-(sinx)^2f(π/12)=(cos(π/12))^2-(sin(π/12))^2=cos(π/6)=√3/2(2)f(x)=[cos(x-π/6)]

f(x)=cos(2x-π/3)-cos2x=1/2cos2x+√3/2sin2x-cos2x=√3/2sin2x-1/2cos2x=sin(2x-π/6)最小正周期T=2π/2=π(2)0

首先：（1）f(-1)=a-b+1=0b=a+1从f(-1)=0,f(x)的值都是正的,可以得到抛物线一定是开口向上的,所以a>0.又：f(x)=ax^2+(a+1)x+1=a(x^2+[(a+1)/

f(x)=2sin(x-π/6)cosx+2cos²x=(2sinxcosπ/6-2cosxsinπ/6)cosx+2cos²x=√3sinxcosx-cos²x+2co

(1)∵cos2x=2cos^2x-1∴f(x)=1/2+cos(2x+π/6)/2对称轴2x0+π/6=π+2kπx0=5π/12+kπg(x0)=1+1/2sin(5π/6+2kπ)=5/4（2）

f(x)＝√3sin2x＋cos2x＝2sin(2x＋π/6)∴f(x0)＝2sin(2x0＋π/6)＝6/5∴sin(2x0＋π/6)＝3/5∵x0∈[π/4,π/2]∴2x0＋π/6∈[2π/3,

解f(x)=2cos^2x+2√3sinxcosx-1=√3sin2x+cos2x=2sin(2x+π/6)∴最小正周期为：2π/2=π再答：不懂追问再问：在三角形ABC中，角ABC所对的边分别是ab