△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状(2)若sinB>△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状2)若sinB>(根号3)/2,求角C的取值范围.
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![△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状(2)若sinB>△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状2)若sinB>(根号3)/2,求角C的取值范围.](/uploads/image/z/1626113-65-3.jpg?t=%E2%96%B3ABC%E4%B8%AD%2C%E4%B8%89%E5%86%85%E8%A7%92A%2CB%2CC%E6%BB%A1%E8%B6%B3sinA%EF%BC%88cosB%2BcosC%EF%BC%89%3DsinB%2BsinC%2C%281%29%E5%88%A4%E6%96%AD%E4%B8%89%E8%A7%92%E5%BD%A2%E7%9A%84%E5%BD%A2%E7%8A%B6%EF%BC%882%EF%BC%89%E8%8B%A5sinB%3E%E2%96%B3ABC%E4%B8%AD%2C%E4%B8%89%E5%86%85%E8%A7%92A%2CB%2CC%E6%BB%A1%E8%B6%B3sinA%EF%BC%88cosB%2BcosC%EF%BC%89%3DsinB%2BsinC%2C%281%29%E5%88%A4%E6%96%AD%E4%B8%89%E8%A7%92%E5%BD%A2%E7%9A%84%E5%BD%A2%E7%8A%B62%EF%BC%89%E8%8B%A5sinB%3E%EF%BC%88%E6%A0%B9%E5%8F%B73%EF%BC%89%2F2%2C%E6%B1%82%E8%A7%92C%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状(2)若sinB>△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状2)若sinB>(根号3)/2,求角C的取值范围.
△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状(2)若sinB>
△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,
(1)判断三角形的形状
2)若sinB>(根号3)/2,求角C的取值范围.
△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状(2)若sinB>△ABC中,三内角A,B,C满足sinA(cosB+cosC)=sinB+sinC,(1)判断三角形的形状2)若sinB>(根号3)/2,求角C的取值范围.
(1)由余弦定理和正弦定理:
sinA(cosB+cosC)=sinB+sinC
==>a/R[(a^2+c^2-b^2)/2ac+(a^2+b^2-c^2/2ab)]=b/R+c/R
==>(a^2+c^2-b^2)/2c+(a^2+b^2-c^2/2b)=b+c
==>b(a^2+c^2-b^2)+c(a^2+b^2-c^2)=2bc(b+c)
==>ba^2-bc^2-b^3+ca^2-cb^2-c^3=0
==>(ba^2+ca^2)-(bc^2+c^3)-(b^3-cb^2)=0
==>a^2(b+c)-c^2(b+c)-b^2(b+c)=0
==>(b+c)(a^2-c^2-b^2)=0
==>a^2=c^2+b^2
所以,三角形是直角三角形.
(2)在直角三角形中,A=90°,得0°