Question

Pomogite 3 zadachu rewit...

Answer 1

Сделаем замену 
$arcsin(-\frac{1}{4})= \alpha$
тогда 
$tg(\alpha+90а)=ctg \alpha \\ ctg \alpha =\frac{cos \alpha }{sin \alpha }$
а так как $cos(arccos \beta )= \beta$ то 


$\frac{cos \alpha }{sin \alpha } = \frac{cos(arcsin-\frac{1}{4})}{sin(arcsin-\frac{1}{4})}\\ sina=-\frac{1}{4}\\ cosa=\sqrt{1-\frac{1}{4}^2}=\frac{\sqrt{15}}{4}\\ ctga=\frac{\frac{\sqrt{15}}{4}}{\frac{1}{4}}=\sqrt{15}$
Ответ  $\sqrt{15}$