因为b^2sin^2C=c^2sin^2B=bcCOSB^COSC,所以b^2/c^2=sin^2B/sin^2C,b/c=cosB^cosC/sin^2C=cosB/sinCtanC,所以cos^2B/sin^2Ctan^2C=sin^2B/sin^2C,所以cos^2B/tan^2C=sin^2B,所以cos^2B=sin^2B,tan^2C=1,解得角B=45度,角C=45度,所以三角形ABC为等要三角形.我的回答完毕,如果还有哪些不明白的地方可以继续问,我会尽量为您解答.