已知三角形ABC的内角A.B.C的对边分别为a,b,c,且满足sin(2A+B)/sinA=2+2cos...
问题描述:
已知三角形ABC的内角A.B.C的对边分别为a,b,c,且满足sin(2A+B)/sinA=2+2cos...
已知三角形ABC的内角A.B.C的对边分别为a,b,c,且满足sin(2A+B)/sinA=2+2cos(A+B) (1)证明,b=2a (2)若c=√7a,求∠C大小
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答
(1)sin(2A+B)/sinA=2+2cos(A+B)sin(2A+B)=2sinA+2sinAcos(A+B)sin2AcosB+sinBcos2A=2sinA+2sinA(cosAcosB-sinAsinB)2sinAcosAcosB+sinBcos2A=2sinA+2sinAcosAcosB-2sinAsinAsinBsinBcos2A+2sinBsinAsinA=2sinA有二倍...