a |
sinA |
b |
sinB |
c |
sinC |
从而a=2RsinA,b=2RsinB,∴2RsinA>2RsinB,∴sinA>sinB.∴选项A正确.
y=cosx在(0,π)上是减函数,∵0<A<π,0<B<π,且A>B,∴cosA<cosB.∴选项B正确.
取A=60°,B=45°,则sin2A=sin120°=
| ||
2 |
∵A+B+C=π,∴sin(A+B)=sinC,∵0<A-B<π,∴sin(A-B)>0,又sinC>0,
∴cos2A-cos2B=-2sin(A+B)sin(A-B)=-2sinCsin(A-B)<0,∴cos2A<cos2B.∴选项D正确.
故选C.