Оба уравнения решаются как однородные.
3.33 1 + Cos4xSin4x = Cos²4x
Sin²4x + Cos²4x + Sin4xCos4x = Cos²4x
Sin²4x + Sin4xCos4x = 0
Sin4x(Sin4x + Cos4x ) = 0
Sin4x = 0 или Sin4x + Cos4x = 0 | : Cos4x
4x = πn , n ∈Z tg4x +1 = 0
x = πn/4, n ∈Z tg4x = -1
4x = -π/4 + πk , k ∈Z
x = -π/16 + πk/4 , k ∈Z
3.34 6Sin²x - SinxCosx - Cos²x = 3*1
6Sin²x - SinxCosx -Cos²x = 3(Sin²x + Cos²x)
6Sin²x - SinxCosx -Cos²x = 3Sin²x + 3Cos²x
3Sin²x - SinxCosx -4Cos²x = 0 | : Cos²x
3tg²x -tgx -4 = 0
tgx = t
3t² - t - 4 = 0
D = 49
t₁ = 8/6 t₂ = -1
tgx = 4/3 tgx = -1
х = arctg(4/3) + πk , k ∈Z x = -π/4 + πn , n ∈Z