已知tanx=4,求1 2sin2x 2 3cos2x

sin(2x)=2tanx/(1+tan²x)=3/5sin²(x+π/4)=[1-cos(2x+π/2)]/2=(1/2)+sin(2x)/2=(1/2)+(1/2)(3/5)=

/>∵(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

snx/cosx=tanx=3sinx=3cosx代入sin²x+cos²x=1所以cos²x=1/10sin²x=9/10sinxcosx=(3cosx)co

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

sin2x=2sinx*cosx=2sinx/cosx*cos^2x=2tanx/(1/cos^2x)=2tanx/[(sin^2x+cos^2x)/cos^2x]=2tanx/(1+tan^2x)2

tanx=2平方得sin²x=4cos^2x5cos^2x=1cos^2x=1/5sin^2x=4/5sinxcosx=√[sin^2xcos^2x]=2/5(2/3)sin^2x+(1/4

17π/12＜x＜7π/4,得5π/3＜x+π/4＜2πcos(x-π/4)=cos[(x+π/4)-π/2]=sin(x+π/4)=-√[1-sin²(x+π/4)]=-√[1-(3/5)

cos(x+y)cosy+sin(x+y)siny=cos((x+y)-y)=cosx=4/5sinx=正负3/5tanx=正负3/4

tanx=sinx/cosx=-4,sinx=-4cosx又sin^2x+cos^2x=1得sin^2x=16/17sinxcosx=sin^2x/(sinx/cosx)=16/17/(-4)=-4/

cos(π/4-x)=-4/5得(√2/2)(cosx+sinx）=-4/5所以cosx+sinx=-4√2/5-----------（1）cos(π/4+x)=sin(π/2-π/4-x)=sin(

sin（π/4+x）=(√2/2sinx+√2/2cosx)=1/2(sinx+cosx)=(sinx+2sinxcosx+cosx)/2=(sinx+2sinxcosx+cosx)/(2sinx+2

因为tanx=3所以sinx,cosx同号.sin^2x=9/10,cos^2x=1/10所以原式=2/3*9/10+1/4*1/10=3/5+1/40=5/8

1、sin(x-45)=sinxcos45-cosxsin45=√2/2*(sinx-cosx)=√2/4sinx-cosx=1/2平方sin²x+cos²x-2sinxcosx=

,而sin^2a+cos^2a=1,得sin^2a=4/5f(x)=(1+1/tanx)sin^2-2sin(x+π/4)sin(x-π/4).=sinx(cosx+sinx)+2sin(x+π/4)

1.证明:角BAC为直角,即,证明:向量AB*向量AC=0,即可,向量AB*向量AC=(1+tanx)*sin(x-π/4)+(1-tanx)*sin(x+π/4)=[sin(x-π/4)+sin(x

由tanX/（tanX-1）=-1得tanX=1/2sinX的平方+sinXcosX+2=（sinX的平方+sinXcosX+2（sinX的平方+cosX的平方))/（sinX的平方+cosX的平方)

sinx=-1/3,有（sinx）^2+(cosx)^2=1得cosx=√（1-sinx^2）=2√2/3或者-2√2/3tanx=sinx/cosx=（-1/3）/（2√2/3）=-√2/4或者ta

tanx=3/4sin(π-x)=-3/5

原式=(2sinxcosx-2sin²x)/(1-sina/cosx)=2sinx(cosx-sinx)/[(cosx-sinx)/cosx)]=2sinxcosx=sin2x=-cos(π

(sin2x-2sin^2x)/(1-tanx)=[2sinx*(cosx-sinx)]/[1-sinx/cosx]=[2sinx*(cosx-sinx)]/[(cosx-sinx)/cosx]=2s