2 cos3x+căn3.sinx+cosx=0 giúp e vs

Đáp án: \(\left[ \begin{array}{l}x = -\dfrac{π}{6} – kπ\\x = \dfrac{π}{12} + k\dfrac{π}{2}\end{array}\right.\) `(k ∈ ZZ)`

Giải thích các bước giải:

`2cos 3x + sqrt{3}sin x + cos x = 0`

`<=> (\sqrt{3})/(2)sin x + 1/(2)cos x = -cos 3x`

`<=> cos (x – π/3) = cos 3x`

`<=>` \(\left[ \begin{array}{l}x – \dfrac{π}{3} = 3x + k2π\\x – \dfrac{π}{3} = -3x + k2π\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x = -\dfrac{π}{6} – kπ\\x = \dfrac{π}{12} + k\dfrac{π}{2}\end{array}\right.\) `(k ∈ ZZ)`