Câu 1
1. sin(2x - 1) = sin(3x + 1)
<=> 3x + 1 = 2x - 1 + k2π hoặc 3x + 1 = π - 2x + 1 + k2π, k nguyên
<=> x = -2 + k2π hoặc x = π/5 + k2π/5, k nguyên
2. cos(x - π/4) = cos(2x + π/2)
<=> 2x + π/2 = x - π/4 + k2π
hoặc 2x + π/2 = π/4 - x + k2π, k nguyên
<=> x = -3π/4 + k2π
hoặc x = -π/12 + k2π/3, k nguyên

3. ĐKXĐ cos(2x + π/3) khác 0
       tan(2x + π/3) = tanπ/3
<=> 2x + π/3 = π/3 + kπ
<=> x = kπ/2, k nguyên
4. ĐKXĐ sin(45° - x) khác 0
      cot(45° - x) = √3 /3
<=> cot(45° - x) = cot60°
<=> 60° = 45° - x + k.180°, k nguyên
<=> x = -15° + k.180°, k nguyên

5. sin2x = √3 /2
<=> sin2x = sinπ/3
<=> 2x = π/3 + k2π
hoặc 2x = 2π/3 + k2π, k nguyên
<=> x = π/6 + kπ
hoặc x= π/3 + kπ, k nguyên
6. cos(2x + 25°) = -√2 /2
<=> cos(2x + 25°) = cos135°
<=> 2x + 25° = 135° + k.360°
hoặc 2x + 25° = -135° + k.360°, k nguyên
<=> x = 55° + k.180°
hoặc x = -80° + k.180°, k nguyên

7. sin3x = sinx
<=> 3x = x + k2π
hoặc 3x = π - x + k2π, k nguyên
<=> x = kπ
hoặc x = π/4 + kπ/2, k nguyên
8. cot(4x + 2) = -√3
<=> cot(4x + 2) = cot(-π/6)
<=> 4x + 2 = -π/6 + kπ, k nguyên
<=> x = -π/24 - 1/2 + kπ/4, k nguyên

9. tan(x + 15°) = √3 /3
<=> tan(x + 15°) = tan30°
<=> x + 15° = 30° + k.180°, k nguyên
<=> x = 15° + k.180°, k nguyên
10. sin(8x + 60°) + sin2x = 0
<=> sin(8x + 60°) = -sin2x
<=> sin(8x + 60°) = sin(-2x)
<=> 8x + 60° = -2x + k.360°
hoặc 8x + 60° = 180° + 2x + k.360°, k nguyên
<=> x = -10° + k.36°
hoặc x = 20° + k.60°, k nguyên

11. cosx/2 = -cos(2x - 30°)
<=> cosx/2 + cos(2x - 30°) = 0
<=> 2.cos(5x/4 - 15°).cos(3x/4 - 15°) = 0
<=> cos(5x/4 - 15°) = 0 hoặc cos(3x/4 - 15°) = 0
<=> 5x/4 - 15° = 90° + k.180° hoặc 3x/4 - 15° = 90°+ k.180°
<=> x = 84° + k.144° hoặc x = 140° + k.240°, k nguyên
12. sinx - cos2x = 0
<=> sinx = cos2x
<=> cos2x = cos(π/2 - x)
<=> 2x = π/2 - x + k2π
hoặc 2x = x - π/2 + k2π, k nguyên
<=> x = π/6 + k2π/3
hoặc x = -π/2 + k2π, k nguyên

13. tanx = cot(π/4 - 2x)
<=> sinx/cosx = cos(π/4 - 2x)/sin(π/4 - 2x)
<=> sinx.sin(π/4 - 2x) = cosx.cos(π/4 - 2x)
<=> -1/2.[cos(π/4 - x) - cos(3x - π/4)] = 1/2.[cos(π/4 - x) + cos(3x - π/4)
<=> 1/2.cos(3x - π/4) - 1/2.cos(π/4 - x) = 1/2.cos(π/4 - x) + 1/2.cos(3x - π/4)
<=> cos(π/4 - x) = 0
<=> π/4 - x = π/2 + kπ, k nguyên
<=> x = -π/4 - kπ, k nguyên
14. sin2x = cos3x
<=> cos3x = cos(π/2 - 2x)
<=> 3x = π/2 - 2x + k2π
hoặc 3x = 2x - π/2 + k2π, k nguyên
<=> x = π/10 + k2π/5
hoặc x = -π/2 + k2π, k nguyên

15. sin(x - 2π/3) = cos2x
<=> cos2x = cos(5π/3 - x)
<=> 2x = 5π/3 - x + k2π
hoặc 2x = x - 5π/3 + k2π, k nguyên
<=> x = 5π/9 + k2π/3, k nguyên
hoặc x = -5π/3 + k2π, k nguyên
16. sin4x = -cosx
<=> sin(-4x) = cosx
<=> cos(4x + π/2) = cosx
<=> 4x + π/2 = x + k2π
hoặc 4x + π/2 = -x + k2π, k nguyên
<=> x = -π/6 + k2π/3
hoặc x = -π/10 + k2π/5, k nguyên

17. sin5x = -sin2x
<=> sin5x = sin(-2x)
<=> 5x = -2x + k2π
hoặc 5x = π + 2x + k2π, k nguyên
<=> x = k2π/7
hoặc x = π/3 + k2π/3, k nguyên
18. sin^2(2x) = sin^2(3x)
<=> 1 - 2sin^2(2x) = 1 - 2sin^2(3x)
<=> cos4x = cos6x
<=> 6x = 4x + k2π
hoặc 6x = -4x + k2π, k nguyên
<=> x = kπ
hoặc x = kπ/5, k nguyên

19. tan(3x + 2) + cot2x = 0
<=> tan(3x + 2) = -cot2x
<=> sin(3x + 2)/cos(3x + 2) = -cos2x/sin2x
<=> -sin2x.sin(3x + 2) = cos2x.cos(3x + 2)
<=> 1/2.(cos(5x + 2) - cos(x + 2)] = 1/2.(cos(5x + 2) + cos(x + 2)]
<=> cos(x + 2) = 0
<=> x + 2 = π/2 + kπ, k nguyên
<=> x = π/2 - 2 + kπ, k nguyên
20. sin4x + cos5x = 0
<=> cos5x = sin(-4x)
<=> 5x = -4x + k2π
hoặc 5x = 4x + k2π, k nguyên
<=> x = k2π/9 hoặc x = 2π, k nguyên

21. 2sinx + √2.sin2x = 0
<=> sinx + √2.cosx.sinx = 0
<=> sinx(1 + √2.cosx) = 0
<=> sinx = 0 hoặc cosx = -1/√2 = cos3π/4
<=> x = π/2 + kπ
hoặc x = 3π/4 + k2π hoặc x = -3π/4 + k2π, k nguyên
22. sin^2(2x) + cos^2(3x) = 1
<=> sin^2(2x) = sin^2(3x)
<=> 1 - 2sin^2(2x) = 1 - 2sin^2(3x)
<=> cos4x = cos6x
<=> 6x = 4x + k2π
hoặc 6x = -4x + k2π, k nguyên
<=> x = kπ
hoặc x = kπ/5, k nguyên

23. sin5x.cos3x = sin6x.cos2x
<=> 1/2.(sin8x + sin2x) = 1/2.(sin8x + sin4x)
<=> sin2x = sin4x
<=> 4x = 2x + k2π
hoặc 4x = π - 2x + k2π, k nguyên
<=> x = kπ
hoặc x = π/6 + kπ/3, k nguyên
24. cosx - 2sin^2(x/2) = 0
<=> cosx - 1 + 1 - 2sin^2(x/2) = 0
<=> cosx - 1 + cosx = 0
<=> 2cosx - 1 = 0
<=> cosx = 1/2 = cosπ/3
<=> x = ±π/3 + k2π, k nguyên