sin2a等于sin2b

喜欢你的求学态度.有公式sin2x=sinxcosxsosinAcosA=sinBcosB即1/2sin2A=1/2sin2B即sin2A=sin2B

根据正弦定理asinA=bsinB=csinC=2R，化简已知的等式得：a2=b2+bc+c2，即b2+c2-a2=-bc，∴根据余弦定理得：cosA=b2+c2−a22bc=-12，又A为三角形的内

sin2A+sin2B+sin2C=sin2A+sin2B+sin2(π-A-B)=sin2A+sin2B+sin(2π-2A-2B)=sin2A+sin2B+sin(-2A-2B)=sin2A+si

sin2A-sin2B=0所以sinA=sinB所以∠A=∠B或∠A∠B互补如果互补cos(A+B)=cos180°=0cos(A+B)sin(A-B)=0如果相等sin(A-B)=sin0°=0co

由tan(A+B)=3tanA可以得到：sin(A+B)cosA=3sinAcos(A+B)展开,得(sinAcosB+cosAsinB)*cosA=3sinA*(cosAcosB-sinAsinB)

∵sinAcosA=cosBsinB∴sin2A=sin2B中间省略步骤如下根据倍角公式sin2a=2sinacosa∵sinAcosA=cosBsinB两边乘2得2sinAcosA=2cosBsin

2sin(a+b)cos(a-b)=2(sinacosb+sinbcosa)(cosacosb+sinasinb)=2(sinacosacos^2b+sin^2asinbcosb+sinbcosbco

sin2A=2sinAcosA,sin2B=2sinBcoBsinAcosA=sinBcosB两边同乘以2,得：2sinAcosA=2sinBcosBsin2A=sin2B

两边乘以22sinacosa=2sinbcosb因为sin2x=2sinxcosx所以2sinacosa=2sinbcosb则sin2a=sin2

sin2A=2sinAcosAsin2B=2sinBcosB

左边展开为1/2(2sinAcosA+2sinBcosB)=sinAcosA+sinBcosB右边展开为(sinAcosB+cosAsinB)(cosAcosB+sinAsinB)=sinAcosA(

tan(a+b)tan(a-b)=-1tan^2a-tan^2b=-(1-tan^2atan^2b)tan^2a+1=tan^2b(1+tan^2a)(tan^2a+1)(tan^2b-1)=0tan

倍角公式：sin2A=sin(A+A)=sinAcosA+sinAcosA=2sinAcosAsinAcosA=sinBcosB2sinAcosA=2sinBcosBsin2A=sin2B

第一问算对,就不用详解了吧,设sinA=7m,sinB=5m,sinC=3m就可以算出cosA,cosB,cosC.第二问应该错了cosA=-1/2cosB=11/14cosC=13/14sinA=±

(tanA+tanB)/(1-tanAtanB)=3(tanA-tanB)/(1+tanAtanB)==>2tanA-4tanAtanAtanB-4tanB+2tanAtanBtanB=0==>(si

tan(a+b)tan(a-b)=-1tan^2a-tan^2b=-(1-tan^2atan^2b)tan^2a+1=tan^2b(1+tan^2a)(tan^2a+1)(tan^2b-1)=0tan

因为A和B都是大于0小于180,所以sinA和sinB都为正,于是两边同时除以sinAsinB,右边还是0然后有sinAcosA=sin2A*1/2.sinBcosB=sin2B*1/2于是可以得到你

根据正弦定理a^2/(4R^2)=(b^2+c^2+bc)/(4R^2)a^2=b^2+c^2+bcb^2+c^2-a^2=-bcb^2+c^2-a^2/2bc=-1/2cosA=-1/2A=2π/3

sin2A+sin2B+sin2C=2sin(A+B)cos(A-B)+2sinCcosC(注sin(A+B)=sinC,cos(A+B)=-cosC)=2sinC[cos(A-B)-cos(A+B)

(sinA)^2=(sinB)^2+(sinC)^2+cosBcosC+cosA,cosA=-cosBcosC+sinBsinC,sinA=sinBcosC+cosBsinC,展开.(sinBcosC