△ABC的三个内角A,B,C所对的边分别为a,b,c,asinAsinB+bcos^2A=√2a,求b/a.若c^2=b^2+√3a^2,求B

题目

△ABC的三个内角A,B,C所对的边分别为a,b,c,asinAsinB+bcos^2A=√2a,求b/a.若c^2=b^2+√3a^2,求B

答案

bsinA=asinBasinAsinB+bcos²A=√2absin²a+bcos²A=√2ab=√2ab/a=√2(2)b²=2a²c²=b²+√3a² =2a²+√3a²c=a√[2+√3] =a√[(4+2√3)/2] =a(√3+1)/√2余弦定理co...