www.whkt.net > 已知sinA=4/5,π/2<A<π,求sin2A,Cos(A/2)的值

已知sinA=4/5,π/2<A<π,求sin2A,Cos(A/2)的值

∵π/2<b<a<3π/4, ∴0<a-b<π/4,π<a+b<3π/2. ∵cos(a-b)=12/13,sin(a+b)=-3/5, ∴sin(a-b)=√(1-cos(a-b))=5/13, cos(a+b)=-√(1-sin(a+b))=-4/5. 故sin2a=sin[(a+b)+(a-b)] =sin(a+b)cos(a-b)+cos(a+b)sin(a-b) =(-3/5)(12/13)+(-4/5)(5/13) =-56/65, sin2

tan(π/4+a)=1/2(tanπ/4+tana)/(1-tanπ/4*tana)=1/2(1+tana)/(1-tana)=1/21-tana=2+2tanatana=-1/3tana=sina/cosa=-1/3sina=(-1/3)cosasina+cosa=1[(-1/3)cosa]+cosa=1(1/9)cosa+cosa=1(10/9)cosa=1cosa=9/10(sin2a-2cosa)/(1+

tana=sina/cosa=3所以:sina=3cosa;代入下式sin2a/cosa=2sina/cosa=6故选:d.

解:tana=-4,所以a可在第二象限或第四象限; 所以sina=±4/√17,cosa=±1/√17 a在第二象限时, sin^2a=(4/√17)^2=16/17; 3sin a*cos a=3*(4/√17)*(-1/√17)=-12/17 cos^2a-sin^2a=(-1/√17)^2-(4/√17)^2=-15/17 a在第四象限时, sin^2a=(-4/

∵π/2≤a≤3π/2∴cos(a+π/4)=3/5>0∵a+π/4>3π/2∴3π/2<a+π/4≤7π/4sin(a+π/4)=-√[1-cos(a+π/4)]=-4/5sina=[sin(a+π/4)-π/4]=√2/2*[sin(a+π/4)-cos(a+π/4)]=√2/2*(-4/5-3/5)=-7√2/10cosa=-√(1-sina)=-√2/10cos2a=2cosa-1=-24/25,sin2a=2sinacosa=7/25∴cos(2a+π/4)=√2/2(cos2a-sin2a)=-31√2/5

《1》tan(a-π/4)=[tana-tan(π/4)]/[1+tana*tan(π/4)] =(tana-1)/(1+tana)=-2所以tana=-1/3,因为1+tan^a=1/cos^a,a b∈(3π/4,π),所以cosa=(3√ 10)/10,sina=√ 10/10所以sin2a=2sinacosa=2*(3√ 10)/10*√ 10/10=3/5《2》因为a b∈(3π/4,π),所以(a+b)∈(3π/2,2π),及cos(a+b)=4/5,所以tan(a+b)=-3/4,tan(b+π/4)=tan[(a+b)-(a-π/4)]所以tan(b+π/4)=1/2

tan2a=-2√2;tan2a=2tan a/(1-tan a*tan a )=-2√2化简得到 tan a*tan a -(√2/2)*tan a -1=0解出 tan a =-√2/2 或 tan a =√2由于2a属于(π/2,π),a属于(π/4,π/2),因此tan a =√2(2cos平方a/2-sina-1)/(√2sin(a+π/4)=(cosa -sina)/([√2(sina*cosπ/4+

tana/2=1/2sina=2tana/(1+tan^2a)=4/5cosa=3/5cos(β-a)=√2/10 sin(β-a)=4√6/10sinβ=sin(β-a+a)=sin(β-a)cosa+cos(β-a)sina=4√6/10*3/5+√2/10 *4/5=2(√6+√2)/25

3π/40因为sinx+cosx=1所以sin(a-π/4)=4/5tanπ/4=1所以(tana-1)/(1+tana)=tan(a-π/4)=sin(a-π/4)/cos(a-π/4)=-4/3cos(a-π/4)=-3/5cos[2(a-π/4)]=2cos(a-π/4)-1=-7/25cos(2a-π/2)=-7/25sin2a=cos(2a-π/2)=-7/25所以原式=28/75

1、解: 由tan(a/2)+1/tan(a/2)=tan(x/2)+cot(x/2)=5/2 则: sin(x/2)/cos(x/2)+cos(x/2)/sin(x/2)=5/2 [sin^2(x/2)+cos^2(x/2)]/[sin(x/2)cos(x/2)]=5/2 2/[2sin(x/2)cos(x/2)=5/2 2/sin(x)=5/2 5sin(x)=4 sin(x)=4/5 由于0 <x< Л/2 则: cos(x)>0 则: cos(x)=根

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