Question

решите уравнение
- tgx+ 24ctg = 2

Answer 1

u = tgx

-u + 24/u = 2

u^2 + 2u - 24 = 0

(u - 4)(u + 6) = 0

tgx = u = {-6, 4}

x = {-arctg6 + Пk, arctg4 + Пk}

Answer 2

$-tgx+24, ctgx=2\\-tgx+frac{24}{tgx}-2=0\\frac{-tg^2x-2, tgx+24}{tgx}=0; ,; ; tgxne 0; ; to ; ; xne pi n,; nin Z\\tg^2x+2, tgx-24=0\\t=tgx; ,; ; t^2+2t-24=0; ,; ; D/4=1+24=25; ,; t_{1,2}=-1pm 5\\t_1=-6; ,; ; t_2=4\\a)tgx=-6; ,; ; underline {x=-arctg6+pi n,; nin Z}\\b); ; tgx=4; ,; ; underline {x=arctg4+pi k,; kin Z}$