Giải phương trình ({mathop{rm s}nolimits} {rm{in3}}x + sqrt 3 cos 3x = 2sin x)

Ta có: ({mathop{rm s}nolimits} {rm{in3}}x + sqrt 3 cos 3x = 2sin x ) ( Leftrightarrow 2left( {frac{1}{2}sin 3x + frac{{sqrt 3 }}{2}cos 3x} right) = 2sin x) (Leftrightarrow 2sin left( {3x + dfrac{pi }{3}} right) = 2sin x)

( Leftrightarrow sin left( {3x + dfrac{pi }{3}} right) = sin x) ( Leftrightarrow left[ begin{array}{l}3x + dfrac{pi }{3} = x + k2pi \3x + dfrac{pi }{3} = pi  – x + k2pi end{array} right. ) (Leftrightarrow left[ begin{array}{l}x =  – dfrac{pi }{6} + kpi \x = dfrac{pi }{6} + kdfrac{pi }{2}end{array} right.;left( {k in mathbb{Z}} right))

Chọn đáp án B.