Подскажите, как из [latex] \frac{sin \alpha -cos \beta }{sin \beta +cos \alpha } [/latex] получить [latex] \frac{sin \beta -cos \alpha }{sin \alpha +cos \beta } [/latex]

[latex] \frac{sin \alpha -cos \beta }{sin \beta +cos \alpha } = \frac{(sin \alpha -cos \beta)(sin \alpha +cos \beta )}{(sin \beta +cos \alpha)(sin \alpha +cos \beta )}= \frac{sin^2 \alpha -cos^2 \beta }{(sin \beta +cos \alpha)(sin \alpha +cos \beta )} = \\ = \frac{1-cos^2 \alpha -1+sin^2 \beta }{(sin \beta +cos \alpha)(sin \alpha +cos \beta )}= \frac{(sin \beta -cos \alpha )(sin \beta +cos \alpha )}{(sin \beta +cos \alpha)(sin \alpha +cos \beta )}= \frac{sin \beta -cos \alpha }{sin \alpha +cos \beta } [/latex]