Вычислите ; tg9 градусов - tg 63градусов+tg 81 градусов -tg 27градусов

Question

Алгебра: Вычислите ; tg9 градусов - tg 63градусов+tg 81 градусов -tg 27градусов

zhenianet · Answer

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