Câu h

Câu o

a. cos(2x + π/3) = -1/3
<=> 2x + π/3 = arccos(-1/3) + k2π
hoặc 2x + π/3 = -arccos(-1/3) + k2π, k nguyên
<=> x = (arccos(-1/3))/2 - π/6 + kπ
hoặc x = -(arccos(-1/3))/2 - π/6 + kπ, k nguyên
b. sin(2x) = sin(x + π/6)
<=> 2x = x + π/6 + k2π
hoặc 2x = 5π/6 - x + k2π, k nguyên
<=> x = π/6 + k2π
hoặc x = 5π/18 + k2π/3, k nguyên

c. cos(2x - 60°) = cos(x + 30°)
<=> 2x - 60° = x + 30° + k.360°
hoặc 2x - 60° = -x - 30° + k.360°, k nguyên
<=> x = 90° + k.360°
hoặc x = 10° + k.120° , k nguyên
d. sin4x = cos3x
<=> sin4x = sin(π/2 - 3x)
<=> 4x = π/2 - 3x + k2π
hoặc 4x = π/2 + 3x + k2π, k nguyên
<=> x = π/14 + k2π/7
hoặc x = π/2 + k2π, k nguyên

e. cos^2x = sin^2(3x - 15°)
<=> sin^2(3x - 15°) = sin^2(90° - x)
<=> 1 - 2sin^2(3x - 15°) = 1 - 2sin^2(90° - x)
<=> cos(6x - 30°) = cos(180° - 2x)
<=> 6x - 30° = 180° - 2x + k.360°
hoặc 6x - 30° = 2x - 180° + k.360°, k nguyên
<=> x =26,25° + k.45°
hoặc x = -37,5° + k.90°, k nguyên
g. sin2x = 1/2 (0 < x < 2π)
<=> sin2x = sinπ/6
<=> 2x = π/6 + k2π hoặc 2x = 5π/6 + k2π, k nguyên
<=> x = π/12 + kπ hoặc x = 5π/12 + kπ, k nguyên
Mà 0 < x < 2π nên x = π/12 ; 5π/12 ; 13π/12 ; 17π/12

h. sin5x + sin3x = 0
<=> sin5x = -sin3x
<=> sin5x = sin(-3x)
<=> 5x = -3x + k2π
hoặc 5x = π + 3x + k2π, k nguyên
<=. x = kπ/4
hoặc x = π/2 + kπ, k nguyên
l. sin(5x - 3π/4) + cos(2x + π/3) = 0
<=> cos(2x + π/3) = -sin(5x - 3π/4)
<=> cos(2x + π/3) = sin(3π/4 - 5x)
<=> cos(2x + π/3) = cos(5x - π/4)
<=> 5x - π/4 = 2x + π/3 + k2π
hoặc 5x - π/4 = -2x - π/3 + k2π, k nguyên
<=> x = 7π/36 + k2π/3
hoặc x = -π/84 + k2π/7, k nguyên

i. sin^2(2x - π/3) = 3/4
<=> 1 - 2sin^2(2x - π/3) = 1 - 2.3/4
<=> cos(4x - 2π/3) = -1/2
<=> cos(4x - 2π/3) = cos(2π/3)
<=> 4x - 2π/3 = 2π/3 + k2π
hoặc 4x - 2π/3 = -2π/3 + k2π, k nguyên
<=> x = π/3 + kπ/2
hoặc x = kπ/2, k nguyên
k. cos(x + π/18) = 2/5
<=> x + π/18 = ±arccos2/5 + k2π, k nguyên
<=> x = ±arccos2/5 - π/18 + k2π, k nguyên

n. sin(x + π/5) = -1/2
<=> sin(x + π/5) = sin(-π/6)
<=> x + π/5 = -π/6 + k2π
hoặc x + π//5 = 7π/6 + k2π, k nguyên
<=> x = -11π/30 + k2π
hoặc x = 29π/30 + k2π, k nguyên
o, ĐKXĐ sin3x khác 0
cot3x = tan2π/5
<=> 3x = arctan2π/5 + kπ, k nguyên
<=> x = (arctan2π/5)/3 + kπ/3, k nguyên