Question

sina/1+cosa+sina/1-cosa
упростить выражение

Answer 1

$\dfrac{\sin \alpha}{1+\cos\alpha}+\dfrac{\sin\alpha}{1-\cos\alpha}=\sin\alpha\left(\dfrac{1-\cos \alpha}{1-\cos^2 \alpha}-\dfrac{1+\cos\alpha}{1-\cos^2\alpha}\right)=\\ \\ =\sin\alpha\times \dfrac{1-\cos\alpha-1-\cos\alpha}{\sin^2\alpha}=\dfrac{-2\cos\alpha}{\sin\alpha}=-2{\rm ctg}\alpha$