Question

решить уравнение
tgx-12ctgx+1=0

Answer 1

tgx-12ctgx+1=0      cosx ≠ 0; sinx ≠ 0
$tgx- frac{12}{tgx} +1=0 \ \ frac{tg^2x-12+tgx}{tgx} =0$
tg²x + tgx - 12 = 0
(tgx + 4)(tgx - 3) = 0
1) tgx = -4
    x₁ = arctg (-4) + πn = -arctg 4 + πn;  n∈Z
2) tgx = 3
    x₂ = arctg 3 + πk;  k∈Z