在三角形ABC中.三内角A,B,C,所对的边分别为a,b,c,若满足a=(√3-1）才,tanB/t

网友回答

由正弦定理a/c=sinA/sinC=√3-1
(2a-c)/c=2a/c-c/c=2sinA/sinC-1
所以tanB/tanC=(sinB/cosB)/(sinC/cosC)=sinBcosC/sinCcosB=2sinA/sinC-1
(sinBcosC+sinCcosB)/sinCcosB=2sinA/sinC
sin(B+C)/sinCcosB=2sinA/sinC
sin(180-A)/sinCcosB=2sinA/sinC
sinA/sinCcosB=2sinA/sinC
0同理,sinC不等于0
约分1/cosB=2
cosB=1/2
B=60度代入tanB/tanC=2sinA/sinC-1
且sinA/sinC=√3-1
√3/tanC=2√3-2-1
tanC=2+√3
C=75度A=180-B-C
所以A=45,B=60,C=75