Question

(2cos^(2)(a)/(2))/(ctg(a)/(4)-tg(a)/(4))

Answer 1

$\frac{2cos^{2} \alpha }{2}:(\frac{ctg \alpha }{4}-\frac{tg \alpha }{4})=cos^{2} \alpha:(\frac{ \frac{1}{tg \alpha } }{4}-\frac{tg \alpha }{4})=cos^{2} \alpha:(\frac{1}{4tg \alpha }-\frac{tg \alpha }{4})=$$cos^{2} \alpha:\frac{1}{2tg 2\alpha }=\frac{cos^{2} \alpha}{2tg 2\alpha }$