急!一道数学题,在线等,20分钟内有加分!帮帮忙!在三角形ABC中,A,B,C的对边分别为a,b,c,如果sin(A-B)/sin(A+B)=2c-b/2c,求sinA
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![急!一道数学题,在线等,20分钟内有加分!帮帮忙!在三角形ABC中,A,B,C的对边分别为a,b,c,如果sin(A-B)/sin(A+B)=2c-b/2c,求sinA](/uploads/image/z/1721609-17-9.jpg?t=%E6%80%A5%21%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%9C%A8%E7%BA%BF%E7%AD%89%2C20%E5%88%86%E9%92%9F%E5%86%85%E6%9C%89%E5%8A%A0%E5%88%86%21%E5%B8%AE%E5%B8%AE%E5%BF%99%21%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CA%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E5%A6%82%E6%9E%9Csin%28A-B%29%2Fsin%28A%2BB%29%3D2c-b%2F2c%2C%E6%B1%82sinA)
急!一道数学题,在线等,20分钟内有加分!帮帮忙!在三角形ABC中,A,B,C的对边分别为a,b,c,如果sin(A-B)/sin(A+B)=2c-b/2c,求sinA
急!一道数学题,在线等,20分钟内有加分!帮帮忙!
在三角形ABC中,A,B,C的对边分别为a,b,c,如果sin(A-B)/sin(A+B)=2c-b/2c,求sinA
急!一道数学题,在线等,20分钟内有加分!帮帮忙!在三角形ABC中,A,B,C的对边分别为a,b,c,如果sin(A-B)/sin(A+B)=2c-b/2c,求sinA
在△ABC中:
sin(A-B)/sin(A+B)
=(sinAcosB-sinBcosA)/sin(A+B)
=[(sinAcosB+sinBcosA)-2sinBcosA]/sin(A+B)
=[sin(A+B)-2sinBcosA]/sin(A+B)
=1-2sinBcosA/sin(A+B)
=1-2sinBcosA/sinC
又∵根据正弦定理:b/sinB=c/sinC
∴(2c-b)/2c
=1-b/2c
=1-sinB/2sinC
又∵sin(A-B)/sin(A+B)=(2c-b)/2c
∴1-2sinBcosA/sinC=1-sinB/2sinC
即2sinBcosA/sinC=sinB/2sinC
解得:cosA=1/4
即sinA=√(1-cos²A)=√15/4
先展开 然后利用正弦定理和余弦定理分别替换sina sinb cosa cosb 就可以求出cosa 然后就可以得到sina了
sin(A-B)/sin(A+B)=2c-b/2c,sin(A-B)/sinc=2sinc-sinb/2sinc, 2sin(A-B)=2sin(A+B)-sinb,
2sin(A-B)-2sin(A+B)=-sinb,2(sinacosb-cosasinb-sinacosb-cosasina)=-4cosasinb=-sinb
cosa=1/4,sina=根号15/4
sin(A-B)/sin(A+B)=sin(A+B-2B)/sin(A+B)=sin(C-2B)/sinC=(c-b/2)/cB=pi/6 C=pi/2 A=pi/3
后面是(2c-b)/w2c对吗?