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