3sinx -4sinxcosx 5cos ^2x =2

3sin^2x-4sinxcosx+5cos^2x=2 3sin^2x-4sinxcosx+5cos^2x = 2cos^2x + 2sin^2 3sin^2x-4sinxcosx+5cos^2x - 2cos^2x - 2sin^2 = 0 sin^2x -4sinxcosx + 3cos^2x = 0 делим на cos^2x tg^2x - 4tgx + 3 = 0 tgx = y y^2 - 4y + 3 = 0 y1 = 3 y2 = 1 подставляем tgx = 3 x = arctg3 + пк, к ∈ z tgx = 1 x = п/4 + пк, к ∈ z