Question

Докажите тождество
$sin2a-ctga=-cos2a*ctga$

Answer 1

$sin2 \alpha -ctg \alpha = \\ =2sin \alpha cos \alpha - \dfrac{cos \alpha }{sin \alpha } = \\ = \dfrac{2sin^2 \alpha cos \alpha -cos \alpha }{sin \alpha } = \\ = \dfrac{cos \alpha (2sin^2 \alpha -1)}{sin \alpha } = \\ =-cos2 \alpha ctg \alpha$