如图三角形ABC,COSB=二分真根号二
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/23 10:03:11
由(sinA+sinB)/sinC=(a+b)/c=cosA+cosB=(b^2+c^2-a^2)/2bc+(a^2+c^2-b^2)/2ac得:a^3+b^3+a^2b+ab^2-ac^2-bc^2
化为c/a=2cosB又c/a=sinC/sinA所以sinC=2sinAcosB因为A+B+C=180sinC=sin(A+B)=sinAcosB+sinBcosA于是sinAcosB=sinBco
由正弦定理,b/sinB=c/sinC得b=sinB·c/sinC代入原式得cosC·sinB·c/sinC=c·cosBsinB·cosC=sinC·cosBsinB·cosC-sinC·cosB=
a=√(10²+5²-2×10×5×cos120°)=5√7cosB×cosC={[10²+(5√7)²-5²]/2×10×5√7}×{[5²
sinAcosA=sinBcosBsin2A=sin2BA=B或2A+2B=180A=B或A+B=90三角形是等腰三角形或直角三角形AC=BC或角C为直角
反例:A=120,B=30,则sinA=cosB=sin60,此三角形显然不是直角三角形
正弦定理a/sinA=b/sinB=>a/b=sinA/sinBa*cosA=b*cosB=>a/b=cosB/cosA则cosB/cosA=sinA/sinB即sinAcosA-cosBsinB=0
证明:设AB切⊙O于点F,BC切⊙O于点E,连接AE,OF,∵AB=AC,⊙O是△ABC的内切圆,⊙A与⊙O外切,∴AE过点O,FO⊥AB,AE⊥BC,∵cosB=13,∴cosB=BEAB=FOAO
有公式cosC=cos(180度-A-B)=-cos(A+B)=-cosA*cosB+sinA*sinB又sinA=3/5,cosB=5/13所以sinB=12/13,cosA=4/5或-4/5代入,
cosB/cosC=-b/(3a+c)=-sinB/(3sinA+sinC)(由正弦定理得到此步)之后,等号左右变形-3cosBsinA-cosBsinC=cosCsinB-3cosBsinA=cos
在三角形ABC中sinA=sin(B+C)所以sinA+cosB=根2/2即sin(B+C)+cosB=根2/2由AC=b=2AB=c=3以及正弦定理a/SinA=b/SinB=c/SinC可知3*s
sinA=sin(A+B)所以有2sin(B+C)*(cosB+cosC)=sinB+sinC2(sinB*cosC+csB*sinC)*(cosB+cosC)=sinB+sinC化解得sin(B+2
sinC=3/5过A作AD垂直BC于D我们知道AD=3/5b,CD=4/5bBD=AD=3/5ba=3/5b+4/5b=7/5bc=3√2/5
(cosA)/a=(cosB)/b=(cosC)/ca/cosA=b/cosB=c/cosCsinA/cosA=sinB/cosB=sinC/cosCtanA=tanB=tanCA=B=C三角形ABC
解由sinC=(sinA+sinB)/(cosA+cosB)即sinA+sinB=sinCcosA+sinCcosB即sin(B+C)+sin(A+C)=sinCcosA+sinCcosB即sinBc
sinAsinB-cosAcosB=-cos(A+B)=cos(180-A-B)=cosC希望有用.
∵cosB/cosA=a/b又:根据正弦定理:a/b=sinA/sinB∴cosB/cosA=sinA/sinB∴cosAsinA=cosBsinB∴2sinAcosA=2sinBcosB∴sin2A
1-cosA=2sin(A/2)^2;1-cosB=2sin(B/2)^2;a/b=sinA/sinB=2sin(A/2)cos(A/2)/2sin(B/2)cos(B/2);所以有2sin(A/2)
(2a-c)cosB=bcosC正弦定理得:(4RsinA-2RsinC)cosB=2RsinBcosC2sinAcosB=sinBcosC+sinCcosB2sinAcosB=sin(B+C)2si
25(做辅助线AN垂直于BC,设AN为X,根据cos<ADC=3/5,可计算出DN=3/4X,BD=33BN=BD+DN,根据cosB=12/13可知AN/DN=5/12,即(3/4X+33)/X=1