4cot^2 x + 5cotx + 1 = 0
<=> Cotx = -1/4 hoặc cotx= -1
<=> x = arccot (-1/4) + kπ hoặc x = arccot (-1) + kπ

2sin^2(2x) + 3sin2x + 1 = 0
<=> Sin2x = -1/2 hoặc Sin2x = -1
+) Sin2x = -1/2
<=> 2x = -π/6 + kπ2 hoặc 2x =π +π/6 + kπ2
<=> x = -π/12 + kπ Hoặcx = 7π/12 + kπ
+) Sin2x = -1
<=> 2x = -π/2 + kπ2 hoặc 2x =π +π/2 + kπ2
<=> x = -π/4 + kπ Hoặcx = 3π/4 + kπ

+) Cos(x + 45°) = √2/2
<=> Cos (x + 45°) = cos 45°
<=> x + 45° = 45° + k.360°
Hoặc x + 45° = -45° + k.360°
<=> x = k.360°
Hoặc x = -90° + k.360° (k € Z)
+) 4sin2x + 2 = 0
<=> sin2x = -1/2
<=> sin2x = sin )(-π/6)
<=> 2x = -π/6 + k2π
hoặc 2x =π + π/6 + k2π
<=> x = -π/12 + k2π
Hoặc x = 7π/12 + k2π (k € Z)

4cot^2 x + 5cotx + 1 = 0 (Đk: x # kπ)
<=> Cotx = -1/4 hoặc cotx = -1
<=> x = arccot (-1/4) + kπ hoặc x = -π/4 + kπ (k € Z)

2sin^2(2x) + 3sin2x + 1 = 0
<=> Sin2x = -1/2 hoặc Sin2x = -1
+) Sin2x = -1/2
<=> 2x = -π/6 + k2π hoặc 2x = π + π/6 + k2π
<=> x = -π/12 + kπ Hoặcx = 7π/12 + kπ
+) Sin2x = -1
<=> 2x = -π/2 + k2π hoặc 2x = π + π/2 + k2π
<=> x = -π/4 + kπ hoặcx = 3π/4 + kπ (k € Z)

√3sin2x - √3cos2x = √3
=> sin2x - cos2x = 1
=> √2.sin(2x - π/4) = 1
=> sin(2x - π/4) = 1/√2
=> sin(2x - π/4) = sin( π/4)
=> 2x - π/4 = π/4 + k2π
hoặc 2x - π/4 = π - π/4 + k2π
=> 2x = π/2 + k2π hoặc 2x = π + k2π
=> x = π/4 + kπ hoặc x = π/2 + kπ (k € Z)
Vậy . . .