已知5sinB=sin(2a B)

要证3sinB=sin(2A+B)即证3sin(A+B-A)=sin(A+B+A)即证3sin(A+B)cosA-3cos(A+B)sinA=sin(A+B)cosA+cos(A+B)sinA即证2s

5sinB=sin(2A+B)=sin(A+B+A)=sin(A+B)cosA+cos(A+B)sinA,sinB=sin(A+B-A)=sin(A+B)cosA-cos(A+B)sinA5sin(A

tanc=sinc/cosc=(sinA+sinB)/(cosA+cosB)左分子乘右分母等于右分子乘左分母,并移项得sinAcosC-sinCcosA=sinCcosB-sinBcosC即sin(A

sina+cosb=1/3,平方sin^2a+2sinacosb+cos^2b=1/9sinb-cosa=1/2,平方sin^2b-2cosasinb+cos^2a=1/4相加2-2（sinacosb

sin(a-B)cosa-1/2[sin(2a+B)-sinB]=[sin(a-B+a)+sin(a-B-a)]/2-sin(2a+B)/2+sinB/2=sin(2a-B)/2+sin(-B)/2-

sin2a=2tana/[1+(tana)^2]=2*1/[1+1]=1(cos2a)^2=1-(sin2a)^2(cos2a)^2=1-1(cos2a)^2=0cos2a=03sinB=sin(2a

tanb=2分之1sinb/sinb=2分之1cosb=2sinb又因为sinb平方+cosb平方=1联立方程组sinb平方=五分之一因为b属于（0,π）所以sinb=五分之根号五cosb=五分之二倍

1\Sina+cosb=3/4cosa+sinb=5/4(SinA)2+(cosB)2+2sinAcosB=9/16,(cosA)2+(sinB)2+2cosAsinB=25/16两式相加2+2（si

3sinb=sin(2a+b)可得sin(2a+b)-sinb=2sinb由两角正弦差的公式：sin(2a+b)-sinb=2cos[(2a+b+b)/2]sin[(2a+b-b)/2]=2cos(a

sin(a-B)cosa-1/2[sin(2a+B)-sinB]=sin(a-B)cosa-1/2[2cos(a+b)sina]=sin(a-b)cosa-cos(a+b)sina=sinacosbc

题目没写清楚啊.sin和cos哪个角啊?如果是sina=4/5,cosb=5/13的话,sinb=根号下1减去5/13的平方,答案是12/13

5sinB=sin(2A+B)=sin(A+B+A)=sin(A+B)cosA+cos(A+B)sinA,sinB=sin(A+B-A)=sin(A+B)cosA-cos(A+B)sinA5sin(A

由sina+cosb=3/4,∴（sina+cosb）²=9/16,sin²a+2sinacosb+cos²b=9/16（1）由cosa+sinb=-5/4,∴（cosa

首先sin(a+b)=sina*cosb+cosa*sinbsina^2+cosa^2=1sinb^2+cosb^2=1将已知的两个等式平方得1,sina^2+2sina*cosb+cosb^2=1/

5sinB=sin(2A+B)5sin[(A+B)-A]=sin[(A+B)+A]5sin(A+B)cosA-5cos(A+B)sinA=sin(A+B)cosA+cos(A+B)sinA4sin(A

证明：5sin[(A+B)-A]=sin[A+(A+B)]5sin(A+B)cosA-5cos(A+B)sinA=sin(A+B)cosA+cos(A+B)sinA4sin(A+B)cosA=6cos

tana=1a=kπ+π/43sinB=sin(2a+B)=sin(2kπ+π/2+B)=cosB3sinB=cosBsin^2B+cos^2B=1cos^2B=9/10sin^2B=1/10sinB

sin=sinAcosB+cosAsinB=根号2/2（sinA+sinB）cosB=cosA=根号2/2A=B=45°边长b=c=根号2/2ab=c=2a=2根号2

sin²A-sin²B-sin²C=sinBsinCa/sinA=b/sinB=c/sinC则由sin²A-sin²B-sin²C=sinB

a,b为锐角则0