Question

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

Answer 1

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