\[4sin^3x + 4sin^2x + 3sin2x + 6cosx = 0 \]
\[\Leftrightarrow 4sin^2x(sinx + 1) + 6cosx(sinx+1) = 0 \]
\[\Leftrightarrow (sinx+1)(4sin^2x + 6cosx) =0 \]
\[TH1: sinx+1=0 \]
\[\Leftrightarrow sinx=-1 \]
\[\Leftrightarrow x=\frac{-\pi }{2} + k2\pi ( k \in Z) \]
\[TH2: 4sin^2x + 6cosx = 0 \]
\[\Leftrightarrow -2cos^2x+3cosx+2=0 \]
\[\Leftrightarrow cosx = -1/2\]
\[\Leftrightarrow x=+-(\frac{2\pi }{3}) + k2\pi (k \in Z ) \]
4sin^3x + 4sin^2x + 3sin2x + 6cosx = 0
<=> 4sin^2x(sinx + 1) + 6cosx(sinx+1) = 0
<=> (sinx+1)(4sin^2x + 6cosx) =0
*) sinx+1=0 <=> sinx=-1 <=> x=-pi/2 + k2pi , k thuộc Z
*) 4sin^2x + 6cosx = 0 <=> -2cos^2x+3cosx+2=0 <=> cosx = -1/2 <=> x=+-(2pi/3) + k2pi, k thuộc Z