已知△ABC中，sin2A=sin2B+sin2C且b•cosB-c•cosC=0，则△ABC为（ ）
A．直角三角形
B．等腰三角形
C．等腰直角三角形
D．等边三角形
由正弦定理化简sin2A=sin2B+sin2C得：a2=b2+c2，
∴△ABC为直角三角形；
又根据正弦定理化简b•cosB-c•cosC=0得：sinBcosB=sinCcosC，
即sin2B=sin2C，又B和C为锐角，
∴B=C或B+C=90°，即△ABC为等腰三角形或直角三角形，
综上，△ABC为直角三角形．
故选A
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| Ben and Jim are twin 1 . They are nine. They 2 in Shenyang Primary School. They are in 3 class. Every day they 4 school and come back together. Their teacher, Mrs. Green, says to the pupils (小学生) , "Please write a composition (作文) 'My Mother'. Jim is 5 good boy. He writes the composition 6 home. But Ben plays 7 football 8 his friends. The next day Green says to the class, "I read your composition. But two of yours 9 just the same." Ben stands up and says, "Jim and I are twins. We have the same 10 . | |||
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