Способом введения новой переменной
[tex] \frac{1}{tg ^{2}x}- \frac{2}{tgx}=3 [/tex]

tgx·ctgx = 1 ⇒ ctgx = 1/tgx1/tg²x - 2/tgx = 3ctg²x - 2tgx = 3Пусть t = ctgx.t² - 2t = 3t² - 2t - 3 = 0t² - 2t + 1 - 4 = 0(t - 1)² - 2² = 0(t - 1 - 2)(t - 1 + 2) = 0(t - 3)(t + 1) = 0t = -1; 3.Обратная замена:ctgx = -1x = -π/4 + πn, n ∈ Zctgx = 3tgx = 1/3x = arctg(1/3) + πk, k ∈ ZОтвет: x = -π/4 + πn, n ∈ Z; arctg(1/3) + πk, k ∈ Z.