Question

Упростить неравенство 1-cos2a/sin2a

Answer 1

$\frac{1-cos2 \alpha }{sin2 \alpha }= \frac{1-(cos^2 \alpha -sin^2 \alpha )}{2sin \alpha cos \alpha }= \frac{1-cos^2 \alpha +sin^2 \alpha }{2sin \alpha cos \alpha } = \\ \\ = \frac{sin^2 \alpha +sin^2 \alpha }{2sin \alpha cos \alpha }= \frac{2sin^2 \alpha }{2sin \alpha cos \alpha }= \frac{sin \alpha }{cos \alpha }=tg \alpha$