在三角形ABC中,若8*sin^22分之B C-

a/sinA=2R所以a^2+b^2a^2+b^2所以2abcosC

sin^2A+sin^2B=sin^2C利用三角形正弦定理sinA/a=sinB/b=sinC/c显然a^2+b^2=c^2所以边c所对的角C为直角.

sin²A+sin²B=2sin²C由正弦定理a^2+b^2=2c^2代入余弦定理：cosC=(a^2+b^2-c^2)/(2ab)=c^2/(2ab)>0所以：cosC

用正弦定理化作a^2-b^2+c^2=ac整理得到cosB=a^2-b^2+c^2/2ac=1/2B=π/3

sinA/a=sinB/b=sinC/c=rsin^2A=sin^2B+sin^2C得出a^2*r^2=（b^2+c^2）*r^2即a^2=b^2+c^2所以ABC是直角三角形

∵在△ABC中,sin(A+B)=sinC∴sinC·sin(A-B)=sin²Csin(A-B)=sinC又∵sinC=sin(A+B)∴sin(A-B)=sin(A+B)sinAcosB

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锐角三角形,高中数学题做过.

由正弦定理和已知可以得到:a^2=b^2+c^2.所以三角形为直角三角形.

sin方A+sin方B=sin方C根据正弦定理：a/sinA=b/sinB=c/sinC=2Ra^2/(2R)^2+b^2/(2R)^2=c^2/(2R)^2即：a^2+b^2=c^2,符合勾股定理,

sin^2A+sin^2B=sin^2C=sin^2(A+B)=(sinAcosB+sinBcosA)^2=sin^2Acos^2B+sin^2Bcos^2A+2sinAcosAsinBcosB左边减

a²≤b²+c²-bcbc≤b²+c²-a²1/2≤(b²+c²-a²)/2bccosa≥1/2a≤60°

根据正弦定理：a/sinA=b/sinB=c/sinC=2R,R为该三角形外接圆半径,则：a/2R=sinAb/2R=sinBc/2R=sinC因此：sinA:sinB:sinC=a:b:c=3:2:

sin^2A=sin^2B+sin^2C,sinA=2sinBsinC所以sin^2A-sinA=sin^2B+sin^2C-sinA=sin^2B+sin^2C-2sinBsinC即sinA(sin

sin^A+sin^B=1sin^A=1-sin^B=con^Bsin^A-cos^B=(sinA+cosB)(sinA-cosB)=0所以sinA=cosB=sin(90-B)或者sinA=-cos

sin(A/2)=cos((A+B)/2),得sin(A/2)=cos(90度-(C/2))=sin(C/2)就有A/2=C/2或A/2=180度-C/2,故A=C（A+C=360度舍去）,因此三角形

【1】sin方a+sin方b+sin方c=sin方a+sin方b+sin方(180-(a+b))=sin方a+sin方b+sin方(a+b)=sin方a+sin方b+(sina*cosb+cosa*s

选A.因为在三角形ABC中,若sinC=sinA+sinB,又因为sinC=sin(180°-A-B）=sin（A+B）=(sinAcosB+sinBcosA)=sinAcosB+2sinAcosAs

sin^2A+sin^2B+sin^2C=(1-cosA)/2+(1-cosB)/2+(1-cos^2C)=2-cos(A+B)cos(A-B)-cos^2C=2+cosCsoc(A-B)-cos^2

由正弦定理a/sinA=b/sinB=c/sinC=2R,sin²A+sin²B=sin²C两边同乘以4R²得（2RsinA）²+（2RsinB）&#