√3cos^2x+2sinxcosx-√3sin^2x-1=0

`sqrt{3}cos² x + 2sin x.cos x – sqrt{3}sin² x – 1 = 0`

`<=> -sqrt{3}sin² x + 2sin x.cos x + sqrt{3}cos² x = 1`

– Với `cos x = 0`

`=> -sqrt{3} = 1` (không thoả mãn)

– Với `cos x ne 0`

`=> -sqrt{3}tan² x + 2tan x + sqrt{3} = 1 + tan² x`

`<=> (-sqrt{3} – 1)tan² x + 2tan x + sqrt{3} – 1 = 0`

`<=>` \(\left[ \begin{array}{l}tan x = 1\\tan x = \sqrt{3} – 2\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x = \dfrac{π}{4} + kπ\\x = arctan (\sqrt{3} – 2) + kπ\end{array} \right.\) `(k ∈ ZZ)`