Question

докажите тождество
ctga/tga + 1=1/sina

Answer 1

$\frac{ctg \alpha }{tg \alpha } +1 = \frac{cos \alpha }{sin \alpha } : \frac{sin \alpha }{cos \alpha } +1= \frac{cos \alpha }{sin \alpha } * \frac{cos \alpha }{sin \alpha } +1= \frac{cos ^{2} \alpha }{sin ^{2} \alpha } +1=ctg ^{2} \alpha +1=$

$= \frac{1}{sin ^{2} \alpha }$