Tg^2x+4tgx-5=0, - pi/2

Tgx = a

a² + 4a - 5 = 0

D = 16 + 20 = 36

a = - 5 или a = 1

tgx = - 5 tgx = 1

x = - arctg 5 + πn x = π/4 + πk

x = - arctg 5 ∈ ( - π/2; 0) x∉ ( - π/2; 0)

x = - arctg 5, т. е. tg x = - 5 ⇒ ctg x = - 1/5

ctg2x = (ctg²x - 1) / (2 ctg x) = (1/25 - 1) / (-2/5) = 24/25 · 5/2 = 12/5