Упростите выражение ctgt+tg(-t)/cost+sin(-t)+tg(-t)/sint

Question

Упростите выражение ctgt+tg(-t)/cost+sin(-t)+tg(-t)/sint

---

Answer 1

(ctgt-tgt)/(cost-sint)-tgt/sint=(cost/sint-sint/cost):(cost-sint)_sint/cost*1/sint=
=(cos²t-sin²t)/[costsint(cost-sint)-sint/(costsint)=
=(cost-sint)(cost+sint)/[costsint(cost-sint)-1/cost=
=(cost+sint)/costsint-1/cost=(cost+sint-sint)/costsint=cost/costsint=1/sint