5sin^2x+3sinxcosx-3cos^2x=2

5sin^2x+3sinxcosx-3cos^2x=2sin^2x + 2cos^2x

3sin^x + 3sinxcosx - 5cos^2x = 0

Разделим на cos^2x

3tg^2x + 3tgx - 5 = 0 t = tgx

3t^2 + 3t - 5 = 0

D = 9 + 60 = 69

t1 = (-3-корень (69)) / 6 t2 = (-3+корень (69)) / 6

x1 = arctg ((-3-корень (69)) / 6)

x2 = arctg ((-3+корень (69)) / 6)