已知在三角形abc中,sina(sinb cosb)-sinc=0,sinb cos2c=0,求角a.b.c大小

sinA(sinB+ cosB)-sinC=0,
∴sinAsinB+sinAcosB=sin(A+B)=sinAcosB+cosAsinB,
∴sinAsinB=cosAsinB,sinB>0,
∴tanA=1,A=45°.C=135°-B,
sinB+ cos2C=0,
sinB+cos(270°-2B)=0,
sinB-sin2B=0,
cosB=1/2,B=60°,
∴C=75°.