Question

cos 2 альфа/1-sin 2 альфа = ?

Answer 1

Ответ:

$\dfrac{cos2a}{1-sin2a}=\dfrac{cos^2a-sin^2a}{sin^2a+cos^2a-2\, sina\cdot cosa}=\dfrac{(cosa-sina)(cosa+sina)}{(cosa-sina)^2}=\\\\\\=\dfrac{cosa+sina}{cosa-sina}=\dfrac{cosa+cos(\frac{\pi}{2}-a)}{cosa-cos(\frac{\pi}{2}-a)}=\dfrac{2\cdot cos\frac{\pi}{4}\cdot cos(a-\frac{\pi}{4})}{-2\cdot sin\frac{\pi}{4}\cdot sin(a-\frac{\pi}{4})}=-ctg\Big(a-\dfrac{\pi}{4}\Big)$