题目内容
(2011•山东)在△ABC中,内角A,B,C的对边分别为a,b,c.已知
.
(1)求
的值;
(2)若cosB=
,△ABC的周长为5,求b的长.

(1)求

(2)若cosB=

(1)2 (2)2
(1)因为
所以
即:cosAsinB﹣2sinBcosC=2sinCcosB﹣cosBsinA
所以sin(A+B)=2sin(B+C),即sinC=2sinA
所以
=2
(2)由(1)可知c=2a…①
a+b+c=5…②
b2=a2+c2﹣2accosB…③
cosB=
…④
解①②③④可得a=1,b=c=2;
所以b=2


即:cosAsinB﹣2sinBcosC=2sinCcosB﹣cosBsinA
所以sin(A+B)=2sin(B+C),即sinC=2sinA
所以

(2)由(1)可知c=2a…①
a+b+c=5…②
b2=a2+c2﹣2accosB…③
cosB=

解①②③④可得a=1,b=c=2;
所以b=2

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