sin^2A=sin^2B+sin^2C
两边同乘(2R)^2 a^2=b^2+c^2
∴△ABC是Rt三角形且A是直角
sinA=2sinBcosC
1=2sinBcos(90-B)
1=2sinBsinB
sinB=√2/2
B=45
∴△ABC是等腰直角三角形