5sin^2x-17sinx*cosx+4cos^2x+4=0

5 sin^2 x - 17 sinx cosx + 4 cos^2x+4=0

5 sin^2 x - 17 sinx cosx + 4 cos^2x+4sin^2 x+4 cos^2x=0

9 sin^2 x - 17 sinx cosx+8cos^2x=0 / cos^2x, где cosx = [ - 1,1]

9 tg^2 x - 17 tg x + 8 = 0

tg x = t

9t^2-17t+8=0

D=1

t1=1

t2=8/9

tg x = 1 tg x=8/9

x=pi/4+pik, keZ

x=arctg 8/9+pik, keZ

pi-пи