Question

Подскажите, как из $frac{sin alpha -cos beta }{sin beta +cos alpha }$
получить $frac{sin beta -cos alpha }{sin alpha +cos beta }$

Answer 1

$frac{sin alpha -cos beta }{sin beta +cos alpha } = frac{(sin alpha -cos beta)(sin alpha +cos beta )}{(sin beta +cos alpha)(sin alpha +cos beta )}= frac{sin^2 alpha -cos^2 beta }{(sin beta +cos alpha)(sin alpha +cos beta )} = \ = frac{1-cos^2 alpha -1+sin^2 beta }{(sin beta +cos alpha)(sin alpha +cos beta )}= frac{(sin beta -cos alpha )(sin beta +cos alpha )}{(sin beta +cos alpha)(sin alpha +cos beta )}= frac{sin beta -cos alpha }{sin alpha +cos beta }$