Question

3 sin^2 x-2 sin x cos x -cos^2 x =2

Answer 1

3 sin^2 x-2 sin x cos x -cos^2 x =2
3 sin^2 x-2 sin x cos x -cos^2 x =2 *(Sin^2x + Cos^2x)
3 sin^2 x-2 sin x cos x -cos^2 x =2Sin^2x +2Cos^2x
Sin^2x -2SinxCosx -3Cos^2x = 0 | : Cos^2x
tg^2x -2tgx -3 = 0
tgx = t
t²  -2t -3 = 0
по т. Виета  корни -1  и  3
а) tgx = -1
x = -π/4 + πk , k ∈Z
б) tgx = 3
x = arctg3 + πn , n ∈Z