化简[sin(a+b)-2cosasinb]/[cos(a+b)+2sinasinb]

sin(a+b)-2cosasinb
=sinacosb+sinbcosa-2cos2sinb
=sinacosb-sinbcosa
=sin(a-b)
cos(a+b)+2sinasinb
=cosacosb-sinasinb+2sinasinb
=cosacosb+sinasinb
=cos(a-b)
所以:
[sin(a+b)-2cosasinb]/[cos(a+b)+2sinasinb]
=sin(a-b)/cos(a-b)
=tan(a-b)

sin(a+b)-2cosasinb=sinacosb+sinbcosa-2cosasinb
=sinacosb-sinbcosa=sin(a-b)
cos(a+b)+2sinasinb=cosacosb-sinasinb+2sinasinb
=cosacosb+sinasinb=cos(a-b
所以[sin(a+b)-2cosasinb]/[cos(a+b)+2sinasinb]
=sin(a-b)/cos(a-b)
=tan(a-b)