Question

Докажите тождество ctgt(-t)/tgt+ctgt=-cos^2t

Answer 1

$frac{Ctg(-t)}{tgt+Ctgt} =-frac{frac{1}{tgt}} {tgt+frac{1}{tgt}}=- frac{1}{tgt}: frac{1+tg^{2}t} {tgt} =- frac{1}{tgt}* frac{tgt}{1+tg^{2}t}=- frac{1}{1+tg^{2}t} =-Cos ^{2}t\\-Cos^{2}t=-Cos ^{2}t$

Тождество доказано