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 2alpha }=frac{cos^{2} alpha}{2tg 2alpha }$