cosB/sinB + cosC/sinC = 1/sinA
通分
(cosBsinC + sinBcosC)/sinBsinC = 1/sinA
sin(B+C)/sinBsinC = 1/sinA
sinA /sinBsinC = 1/sinA
所以
(sinA)^2 = sinBsinC
用正弦定理 a/sinA = b/sinB = c/sinC = u
两边同乘u^2
即得
a^2 = bc
若cos(B-C)+cosA=1
cos(B-C)+cosA
= cos(B-C) -cos(B+C)
= 2sinBsinC
所以2sinBsinC =1
由（1）知(sinA)^2 = sinBsinC
所以(sinA)^2 = 1/2
sinA = √2/2
因为 a^2 = bc,a为等比中项,不可能为最长边.A不能为钝角
所以A =45°