((2+ căn 3) cosx - 2sin^2(x/2- pi/4))/2cosx-1=1 Giải giúp mình câu 4 với

`{(2+\sqrt{3})cosx-2sin^2(x/2 -pi/4)}/{2cosx-1}=1`

ĐK: `x\ne+-pi/3+k2\pi (kinZZ)`

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

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

`<=>\sqrt{3}cosx+sin2x=0`

`<=>cosx(2sinx+\sqrt{3})=0`

$\Leftrightarrow\left[\begin{matrix} cosx=0\\ sinx=-\sqrt{3}/2\end{matrix}\right.$

$\Leftrightarrow\left[\begin{matrix} x=\pi/2+k\pi\\ \left[\begin{matrix} x=-\pi/3+k2\pi(l)\\ x=4\pi/3+k2\pi\end{matrix}\right.\end{matrix}\right.$