6sin^2x+sin x cos x -cos^2x=2

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