已知cos(x-π 6)=-根号3 3,则cosx cos(x-π 3)-搜答案-智慧作业帮

用三角公式展开：-sinx+cosx=根号2/3,所以你就知道答案了~,

sin(π-x)-cos(π+x)=√2/3由诱导公式得sin(π-x)=sinxcos(π+x)=-cosxsinx+cosx=√2/3(sinx+cosx)^2=2/91+2sinxcosx=2/

/>cos(5π/6+a)=cos[π-(π/6-a)]=-cos(π/6-a)=-√3/3cos²(π/3+a)=cos²[(π/2)-(π/6-a)]=sin²(π/

1f(x)=√3sinπx+cosπx=2（（√3/2）sinπx+（1/2）cosπx）=2sin（πx+π/3）∴最小正周期T=2π/w=2π/π=2值域f（x）∈[-2,2]2-π/2+2kπ＜

1,x=π/4,y=π/3或者x=3π/4,y=2π/32,（2√2-1）/3

根据诱导公式可得cos(5/6π+x)=cos[π-(π/6—x)]=-cos(π/6—x)=-根号3/3,sin平方的(x+π/3)=[1-cos(2x+2π/3)]/2=[1+cos(π/3-2x

》,

令t=sin2x/1+cos²x=2sinxcosx/sin^x+2cos^x,则有1/t=sin^x+2cos^x/2sinxcosx=(sinx/2cosx)+cosx/sinx=tan

∵cos（x-π/6）=-√3/3∴cosx+cos（x-π/3）=cosx+cosxcosπ/3+sinxsinπ/3=cosx+（1/2）cosx+（√3/2）sinx=（3/2）cosx+（√3

cos(x-π/6)=-√3/3cosx+cos(x-π/3)=cos(x-π/6+π/6)+cos(x-π/6-π/6)=cos(x-π/6)cosπ/6-sin(x-π/6)sinπ/6+cos(

cosx+cos(x-派/3)=2cos(2x-π/3)/2cos(x-x+π/3)/2=2cos(x-π/6)×cosπ/6=2×（-√3/3）×√3/2=-1

经济将积极

1.根号2cosx-根号6sinx利用辅助角公式=2根号2(1/2cosx-2分之根号3sinx0=2根号2sin(π/6-x)2.sin(α-β)cosα-cos(β-α)sinα=3/5sin(α

这个不难.（1）f(x)=√3sin(ωx)+cos(ωx+π/3)+cos(ωx-π/3)-1=√3sin(ωx)+1/2cos(ωx)-√3/2sin(ωx)+1/2cos(ωx)+√3/2sin

cos(x-90)=cos(90-x)=sinx=√2/10∴sinx=√2/10再问：cos(X-45)=根号2/10，X属于90到135度，求sinx和sin（2x+60）再答：=cos(x-45

tanx=-4/3tanx=sinx/cosx3sinx=-4cosxsin²x+cos²x=1∴sin2x=2sinxcosx=-24/25cos2x=-7/25cosx=-3/

是sin(x+π/3)cos(x-π/3)+cos(x+π/3)sin(x-π/3)=-(2√2/3)吧?如果是,则上式可化为sin2x=-2√2/3,∵π

f(x)=2cos(2x-π/3)-√3sin(2x)+1=2*(cos(2x)cos(π/3)+sin(2x)sin(π/3))-√3sin(2x)+1=2*cos(2x)/2+2*sin(2x)*

由公式(sina)^2+(cosa)^2=1sin^2(π/6-a)=1-cos^2(π/6-a)=1-(根号3/3)^2=1-1/3=2/3