2sin^2 x - 10cos 2x = 9sin 2x +10 решите

2sin^2 x - 10cos 2x = 9sin 2x +10
2Sin²x - 10(Cos ²x  - Sin²x) = 9*2Sin xCosx +10*1
2Sin²x - 10Cos ²x  +10 Sin²x = 9*2Sin xCosx +10*(Sin²x + Cos²x)
2Sin²x - 10Cos ²x  +10 Sin²x = 9*2Sin xCosx +10Sin²x + 10Cos²x
2Sin²x - 18SinxCosx -20Cos²x = 0
Sin²x - 9SinxCosx -10Cos²x = 0 | : Cos²x ≠0
tg²x - 9tgx -10 = 0
По т. Виета
tgx = 10                                  tgx = -1
x = arctg10 + πk , k ∈ Z           x = -π/4 + πn , n ∈Z