Пожалуйста, докажите тождество !!! Плиииз

[latex] \frac{1-ctg \beta }{1-tg \beta } =-ctg \beta [/latex] [latex] \frac{1- \frac{cos \beta }{sin \beta } }{1- \frac{sin \beta }{cos \beta } } =-ctg \beta [/latex] [latex] \frac{ \frac{sin \beta -cos \beta }{sin \beta } }{ \frac{cos \beta -sin \beta }{cos \beta } } =-ctg \beta [/latex] [latex] \frac{sin \beta -cos \beta }{sin \beta } * \frac{cos \beta }{-(sin \beta -cos \beta )} =-ctg \beta [/latex] [latex]- \frac{cos \beta }{sin \beta } =-ctg \beta [/latex] [latex]-ctg \beta =-ctg \beta [/latex]