Вопрос пользователя:
Вычислить
tg9°-tg63°+tg81°-tg27°
Илюха отвечает:
tg9-tg63+tg81-tg27 =
= tg9+tg81-(tg27+tg63) =
= tg9+tg(90-9) – (tg27+tg(90-27)) =
= tg9+Ctg9 – (tg27+Ctg) =
= 1/(cos9*sin9)-1/(cos27*sin27) =
= 2/sin18 – 2/sin54 =
= 2*(sin54-sin18)/(sin18*cos36) =
= 2*2*sin18*cos36/(sin18*cos36) = 4