5sin^2 x+4sin x cos x-5cos^2 x=2

Question

5sin^2 x+4sin x cos x-5cos^2 x=2

Answer 1

5sin^2x+4sinxcosx-5cos^2 x-2sin^2 x-2cos^2 x=0
3sin^2x+4sinxcosx-7cos^2 x=0 / cos^2x
3tg^2x+4tgx-7=0 | tgx=t
3t^2+4t-7=0
D=16+84=100
t1=-4+10/6=-1
t2=-4-10/6=-7/3
tgx=-1                                 tgx=-7/3
x1=3pi/4 + 2pik                  x3=arctg(-7/3)+2pik
x2=7pi/4 + 2pik                  x4=arctg(-7/3)+pi+2pik