`cot alpha=-3`

`=> cos alpha=-3sin alpha`

`cot alpha=-3`

`=> cot^2 alpha=9`

`=> 1+cot^2 alpha=10`

`=> 1/[sin^2 alpha]=10`

`=> sin^2 alpha=1/10`

Đề

`P=[sin^3 alpha+cos^3 alpha]/[sin alpha-cos alpha]`

`P=[(sin alpha+cos alpha)(1-sin alpha cos alpha)]/[sin alpha-cos alpha]`

`P=[(sin alpha-3sin alpha)(1+3sin^2 alpha)]/[sin alpha+3sin alpha]`

`P=[(-2sin alpha)(1+3sin^2 alpha)]/[4sin alpha]`

`P=[-(1+3*1/10)]/2`

`P=[-13/10]/2`

`P=-13/20`

`->a=13`, `b=20`

`-> a+b=13+20=33`