Докажите тождество ctga/tga + 1=1/sina

[latex] \frac{ctg \alpha }{tg \alpha } +1 = \frac{cos \alpha }{sin \alpha } : \frac{sin \alpha }{cos \alpha } +1= \frac{cos \alpha }{sin \alpha } * \frac{cos \alpha }{sin \alpha } +1= \frac{cos ^{2} \alpha }{sin ^{2} \alpha } +1=ctg ^{2} \alpha +1=[/latex] [latex]= \frac{1}{sin ^{2} \alpha } [/latex]