1-ctg альфа/tg альфа-1

1-ctg $\alpha$ /tg $\alpha$ -1 = (sin $\alpha$ - cos $\alpha$ ) * cos $\alpha$ / (sin $\alpha$ - cos $\alpha$ ) * sin $\alpha$ = cos $\alpha$ /sin $\alpha$ = ctg $\alpha$
ctg $\alpha$ = cos $\alpha$ /sin $\alpha$
tg $\alpha$ = sin $\alpha$ /cos $\alpha$
1-ctg $\alpha$ = sin $\alpha$ - cos $\alpha$ /sin $\alpha$
tg $\alpha$ -1 = sin $\alpha$ - cos $\alpha$ /cos $\alpha$