Toán Lớp 11: Giúp mình với ạ
Cos2x – √3 sin2x = 2cos(π/3-x)
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Toán Lớp 11: Giúp mình với ạ
Cos2x – √3 sin2x = 2cos(π/3-x)
Comments ( 2 )
<=> 2sin(x + π/4) = √2
<=> sin(x + π/4) = √2 /2
<=> sin(x + π/4) = sin(π/4)
=> x + π/4 = π/4 + k2π
<=> x = k2π ,k∈Z
và x + π/4 = π – π/4 + k2π
<=> x = π – π/4 – π/4 + k2π
<=> x = π/2 + k2π ,k∈Z
vậy phương trình có hai nghiệm
x = k2π ,k∈Z
x = π/2 + k2π ,k∈Z
<=> 2sin(x + π/4) = √2
<=> sin(x + π/4) = √2 /2
<=> sin(x + π/4) = sin(π/4)
<=> x + π/4 = π/4 + k2π
<=> x = k2π ,k ∈ Z
Do x + π/4 = π – π/4 + k2π
<=> x = π – π/4 – π/4 + k2π
<=> x = π/2 + k2π ,k∈Z
Vậy pt có 2 nghiệm:
$x = {k2π; π/2 + k2π}$