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