6sin^2x+sin x cos x -cos^2x=2
6sin^2x+sin x cos x -cos^2x=2(sin^2x+cos^2x)
6sin^2x+sin x cos x -cos^2x=2sin^2x+2cos^2x
6sin^2x+sin x cos x -cos^2x-2sin^2x-2cos^2x=0
4sin^2x+sin x cos x -3cos^2x = 0 /:cos^2x≠0
4tg^2x+tgx-3 = 0
Замена tgx=t, t∈(-∞;+∞)
4t^2+t-3 = 0
D=1+48=49
t=(-1+7)/8=3/4
t=(-1-7)/8= -8/8 = -1
Получим:
tgx=3/4⇒ x=arctg(3/4)+pik, k∈Z
tgx= -1⇒ x= -pi/4+pik, k∈Z