6) 3Sin²2x +7Cos2x -3 = 0
3(1 - Cos²2x) +7Cos2x -3 = 0
3 -3Cos²2x +7Cox²2x -3= 0
4Cos²2x = 0
Cos²2x = 0
Cos2x = 0
2x = π/2 + πk , k ∈Z
x = π/4 + π/2*k , k ∈Z
В промежуток [π; 5π/2] попадут х = 7π/4; 9π/4
7) 4 -5Cosx -2Sin²x = 0
4 - 5Cosx -2(1 - Cos²x) = 0
4 -5Cosx -2 +2Cos²x = 0
Cosx = t
2t² -5t +2 = 0
t₁= 2; t₂ = 1/2
а) Сosx = 2 б)Cosx = 1/2
∅ x = +-π/3 + 2πk , k ∈ Z
В промежуток [π/2; 3π] попадают х = 11π/6; 7π/3
8) Sinx + Cos2x = 0
Sinx + 1 - 2Sin²x = 0
Sinx = t
2t² -t -1 = 0
t₁ = 1, t₂= -1/2
а)Sinx = 1 б) Sinx = -1/2
x = π/2 + 2πk , k ∈Z x = (-1) ⁿ⁺¹ * π/6 + πn , n ∈Z
В промежуток [-π/2; -π/8] попадают х= -π/6