Question

Докажите тождество:
Sina/1-cosa + 1-cosa/sina = 2/sina

Answer 1

$\dfrac{\sin \alpha}{1-\cos \alpha}+\dfrac{1-\cos \alpha}{\sin \alpha}=\dfrac{\sin^2\alpha+1-2\cos \alpha+\cos^2\alpha}{(1-\cos \alpha)\sin \alpha}=\\ \\ =\dfrac{2(1-\cos \alpha)}{(1-\cos \alpha)\sin \alpha}=\dfrac{2}{\sin \alpha}$