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High school mathematics compulsory five-person teaching a version
According to sine theorem: b/2R=sinB, c/2R=sinC.

sinB = 4cosAsinC

∴b/2R=4cosA？ (c/2R)

Namely: b=4cosA? c

∴cosA=b/4c

According to cosine theorem: cosA=(b? +c？ -a？ )/2bc

∴(b？ +c？ -a？ )/2bc=b/4c

4c？ 【b？ -(a? -c？ )]=b？ 200 BC

4c(b？ -2b)=2b？ c

4b？ c - 8bc - 2b？ c=0

2b？ c - 8bc=0

2bc(b-4)=0

∵b≠0，c≠0

∴b-4=0, then b=4.

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