Toán Lớp 11: a, 4cosx+3sinx=3
b, 4cosx+3sinx=5
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Toán Lớp 11: a, 4cosx+3sinx=3
b, 4cosx+3sinx=5
Comments ( 1 )
<=> sinx.3/5 + cosx.4/5 = 1 (*)
Do (3/5)^2 + (4/5)^2 = 1 nên đặt
cosa = 3/5 và sina = 4/5
PT (*) trở thành
sinx.cosa + cosx.sina = 1
<=> sin(x + a) = 1
<=> x + a = π/2 + k2π, k nguyên
<=> x = π/2 – arcsin4/5 + k2π, k nguyên
b. sin3x + √3.cos3x = √2
<=> sin3x.1/2 + cos3x.√3/2 = √2 /2
<=> sin3x.cosπ/3 + cos3x.sinπ/3 = sinπ/4
<=> sin(3x + π/3) = π/4 + k2π, k nguyên
<=> 3x + π/3 = π/4 + k2π
hoặc 3x + π/3 = 3π/4 + k2π, k nguyên
<=> x = -π/36 + k2π/3
hoặc x = 5π/36 + k2π/3, k nguyên