DK : [TEX]cos x \not= \frac12[/TEX]
[TEX]\left{ 2 - 2 cos 2x = 4 sin^2 x \\ 1 - 2 sin^2( \frac{x}{2} - \frac{\pi}{4} ) = cos ( x - \frac{\pi}{2}) = sin x [/TEX]
[TEX](pt) \Leftrightarrow sin x - \sqrt{3} cos x + 4sin^2 x = 2 cos x [/TEX]
[TEX]\Leftrightarrow sin ( x - \frac{\pi}{3}) = 2cos^2x + cos x - 2 [/TEX]