Решите уравнение 5sin2x-4sinxcosx+3cos2x=0

5sin2x - 4sinxcosx + 3cos2x=0 5sin2x - 2sin2x + 3cos2x = 0 3sin2x + 3cos2x = 0  делим на 3 cos^2(x) + 2sinxcosx - sin^2(x) = 0  делим на cos^2(x) 1 + 2tgx - tg^2(x) = 0 tg^2(x) - 2tgx - 1 = 0  назначим tg(x) = t t^2 - 2t - 1 = 0  решим D = 4 + 4 = 8 t1 = (2 + 2*[latex] \sqrt{2} [/latex]) / 2 = 1 + [latex] \sqrt{2} [/latex] t2 = (2 - 2*[latex] \sqrt{2} [/latex]) / 2 = 1 - [latex] \sqrt{2} [/latex] tgx = 1 + [latex] \sqrt{2} [/latex] x = arctg(1 + [latex] \sqrt{2} [/latex]) + [latex] \pi [/latex]*n  где n ∈ Z tgx = 1 - [latex] \sqrt{2} [/latex] x = arctg(1 - [latex] \sqrt{2} [/latex]) + [latex] \pi [/latex]*n  где n ∈ Z