4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2

4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2*1

4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2 * (Sin²x + Cos²x)

4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2Sin ²x + 2 Cos²x

2Sin²x + 5SinxCosx - 3Cos²x = 0|: Сos²x≠ 0

2tg²x + 5tgx - 3 = 0

решаем как квадратное:

tgx = - 3 tgx = 1/2

x = - arctg3 + πk, k ∈ Z x = arctg1/2 + πn, n∈Z