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1+CosA=√3/3sinA,sin=6CosBsinBsinC,求B/C的值

∵3sinA+4cosB=6 ∴(3sinA+4cosB)^2=36 ∴[9(sinA)^2+16(cosB)^2+24sinAcosB=36(1) ∵4sinB+3cosA=1 ∴(4sinB+3cosA)^2=1 ∴16(sinB)^2+9(cosA)^2+24cosAsinB=1(2) (1)+(2):9(sinA)^2+16(cosB)^2+24sinAcosB]+[16(sinB)^2+9(cosA)^2+24cosAsinB]=37 ∴...

嗯 三角形内 如果对应边角 a/sina=b/sinb=c/sianc=k a=ksina b=ksinb c=ksinc ab=k^2sina*sinb=c=ksinc 那么 ksina*sinb=sinc 如过要满足 K只能等于1 所以 不能一定保证这个结论成立

(1)、由正弦定理:sinA/a=sinB/b=sinC/c,得:(3c-a)/b=(3sinC-sinA)/sinB=(cosA-3cosC)/cosB,展开移项得:cosBsinA+sinAcosB=3(sinCcosB+cosBsinC); 即:sin(A+B)=3sin(B+C),sinC=3sinA,sinC/sinA=3。 (2)、c/a=sinC/sinA=...

(1) asin2B=√3bsinA sinA·2sinBcosB=√3sinBsinA A、B均为三角形内角,sinA>0,sinB>0 cosB=√3/2 B=π/6 (2) sinB=sin(π/6)=? sinA=√(1-cos2A)=√(1-?2)=2√2/3 sinC=sin(A+B) =sinAcosB+cosAsinB =(2√2/3)·(√3/2)+?·? =(1+2√6)/6

sinA+sinB+sinC=0 cosA+cosB+cosC=0 sinA+sinB=-sinC cosA+cosB=-cosC 平方得 (sinA+sinB)^2=(sinC)^2 (1) (cosA+cosB)^2=(cosC)^2 (2) 两式相加得 1+2sinAsinB+2cosAcosB+1=1 所以 2sinAsinB+2cosAcosB=-1 cos(A-B)=-1/2 (2)-(1) (cosC)^2-...

3sinB^2+3sinC^2-2sinBsinC=3sinA^2 由正弦定理得 a/sinA=b/sinB=c/sinC sinB=b/a ·sinA sinC=c/a ·sinA 化简得 3sinB^2+3sinC^2+3sinA^2=2sinBsinC 3﹙b²/a²﹚sin²A+3﹙c²/a²﹚sin²A+3sin²A=2· ﹙b/a﹚sinA...

a=ksina b=ksinb c=ksinc 所以只要求出k就可以了 s=1/2 b*c*sina =1/2*2*c*sin60=2根号3 c=4 a^2=b^2+c^2-2bccosa=4+16-2*2*4*cos60=20-8=12 a=2根号3 所以k=a/sina=4 所以原式=4

解: ① 由正弦定理得:a/sinA=c/sinC a=csinA/sinC c=√3,sinA=√6sinC代入,得 a=√3·√6sinC/sinC=3√2 a的值为3√2 ② cos(2A)=-⅓ cos²A-sin²A=-⅓,又cos²A+sin²A=1 解得cos²A=⅓ A为锐角,sinA>0,cosA...

(本小题满分12分)(Ⅰ)∵ sinB+sinC sinA = 2-cosB-cosC cosA ∴sinBcosA+sinCcosA=2sinA-cosBsinA-cosCsinA∴sinBcosA+cosBsinA+sinCcosA+cosCsinA=2sinAsin(A+B)+sin(A+C)=2sinA…(3分)sinC+sinB=2sinA…(5分)所以b+c=2a…(6分)(Ⅱ)由...

(1)证明:∵sinB+sinCsinA=2-cosB-cosCcosA,∴sinBcosA+sinCcosA=2sinA-cosBsinA-cosCsinA,∴sinBcosA+cosBsinA+sinCcosA+cosCsinA=2sinA,∴sin(A+B)+sin(A+C)=2sinA,∴sinC+sinB=2sinA,∴b+c=2a;(2)解:∵b+c=2a,b=c,∴a=b=c,∴△ABC为...

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