Ctg a/2 = 2 найдите ctg a

Question

Ctg a/2 = 2
найдите ctg a

Answer 1

1) Ctg a = 1/tg a
2) tg 2a = 2 tg a/( 1 - tg²a)
Ctg a/2 = 2 ⇒ tg a/2 = 1/2
tg a = 2 tg a/2/(1 - tg ² a/2) = 2·1/2 /(1 - 1/4)= 1/ 3/4= 4/3
Сtg a = 3/4