Докажите тождество: ctg t / (tg t + ctg t )=cos2t

(cost/sint)/(sint/cost+cost/sint)=(cost/sint)/((sin^2t+cos^2t)/sint*cost)= [sin^2t+cos^2t=1] = cost/sint * sintcost = 2cost
Получается 2cost=cos2t
Условие верно?