已知sinx cosx=根号2求下列各式的值 sin^4x-cos^4x

f(x)=√3sin²x+sinxcosx=√3[(1-cos2x)/2]+1/2sin2x=1/2sin2x-√3/2cos2x+√3/2=sin(2x-π/3)+√3/2∵x∈[π/2,

f(x)=2cosx*sin(x+π/3)-根号3sinx^2+sinxcosx=2cosx*(1/2sinx+根号3/2cosx)-根号3sinx^2+sinxcosx=2sinxcosx+根号3c

/>∵(1+tanx)/(1-tanx)=3+根号二∴1+tanx=3+√2-（3+√2)tanx∴(4+√2)tanx=2+√2∴tanx=(2+√2)/(4+√2)=(3+√2)/7∴cos

f(x)=1/2-1/2cos2x+√3/2sin2x-1/2=sin(2x-π/6)f(-π/12)=sin(-π/3)=-√3/2(2)-π/6

有sin(x-45°)=√2／4=sinxcos45°-cosxsin45°,得sinx-cosx=0.5,两边平方得1-2sinxcosx=0.25.sinxcosx=3／8.tanx+1／tanx

化简可得f（x）=2sin(2x+Pi/6)-1单调递增区间：-Pi/2

f(x)=2√3sinxcosx+2cos^2x=√3sin2x+cos2x+1=2sin(2x+π/6)+1-π/2+2kπ

f(x)=2√3sinxcosx-cos2x=√3sin2x-cos2x=2(sin2x*√3/2-cos2x*1/2)=2sin(2x-π/6)x=π/12;函数f(x)的图象可以由函数y(x)=2

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

sinxcosx=(1/2)*sin（2x）=(1/2)*{2tanx/[1+(tanx)^2]}=2/5

(sinX+cosX)平方=2所以sinX平方+cosX平方+2sinXcosX=2因为sinX平方+cosX平方=1所以sinXcosX=0.5

f(x)=2√3sinxcosx+2cos^2x=√3*sin2x+cos2x+1=2(√3/2*sin2x+1/2*cos2x)+1=2sin(2x+π/6)+1f(x)的最小正周期T=2π/2=π

解y=2cos^2x+2根号3sinxcosx-1=（1+cos2x）+√3sin2x-1=cos2x+√3sin2x=2（√3/2sin2x+1/2cos2x）=2sin（2x+π/6）即T=2π/

g

1、f(x)=-(cos²x-sin²x)+√3(2sinxcosx)=√3sin2x-cos2x=2sin(2x-π/6)T=2π/2=π递减则2kπ+π/2

根号的括号到哪里啊?要是到（3sinXcosX+2cos^2X）和到根号（3sinXcosX+2cos^2X-1）.要是后一种结果简单一点：根号里面化简得到[3/2sin(2X)+cos(2X)]=（

f(x)=（1/2）2sinx*cosx+√3*cosx^2=1/2sin2x+√3/2（2cos^2-1)+√3/2=1/2sin2x+√3/2cos2x+√3/2=cos60sin2x+cos2x

答：f(x)=2√3sinxcosx+2(cosx)^2-1=√3sin(2x)+cos(2x)=2*[(√3/2)*sin(2x)+(1/2)cos(2x)]=2sin(2x+π/6)最小正周期T=

fx=2根号3sinxcosx+1-2sin^2x=2sin（2x+π/6）周期为π

函数fx=2根号3sinxcosx+1-2sinX=根号3sin2x+cos2x=2sin（2x+30度）,fx的值域就是【-2,2】