Решите однородные тригонометрические уравнения

2sin^2x - 4 = 3sinxcosx - 4cos^2x 2sin^2x - 4 × 1 - 3sinxcosx + 4cos^2x = 0 [ sin^2a + cos^2a = 1 ] 2sin^2x - 4 × ( sin^2x + cos^2x) - 3sinxcosx + 4cos^2x = 0 2sin^2x - 4sin^2x - 4cos^2x - 3sinxcosx + 4cos^2x = 0 | : cos^2x 2tg^2x - 4tg^2x - 4 - 3tgx + 4 = 0 - 2tg^2x - 3tgx = 0 | × (-1) 2tg^2x + 3tgx = 0 tgx ( 2tgx + 3) = 0 tgx = 0 x1 = Пn, n € Z 2tgx + 3 = 0 2tgx = -3 | :2 tgx = -3/2 x = arctg (-3/2) + Пn, n € Z x = - arctg 3/2 + Пn, n € Z