Упростите выражение

(1 + ctg2x ctg x) / (tgx + ctgx)

1+сtg2x*ctgx=1+1/tg2x*1/tgx=1 + (1-tg²x) / (2tgx) * 1/tgx=1 + (1-tg²x) / (2tg²x) =

= (2tg²x+1-tg²x) / (2tg²x) = (1+tg²x) / (2tg²x)

tgx+ctgx=tgx+1/tgx = (tg²x+1) / tgx

(1+tg²x) / (2tg²x) : (tg²x+1) / tgx = (1+tg²x) / (2tg²x) * tgx / (tg²x+1) = 1/[2tgx)