7)ĐKXĐ $x\ne \frac{k\pi}{2}$
$pt\Leftrightarrow 1+\frac{1-\tan^2x}{\tan x}=\frac{4\sin^2x}{\sin^22x}$
$\Leftrightarrow 1+\frac{1-\tan^2x}{\tan x}=\frac{1}{2\cos^2x}$
$\Leftrightarrow 2\left(1+\frac{1-\tan^2x}{\tan x} \right)=1+\tan^2x$
$\Leftrightarrow \left[ \begin{array}{l} \tan x=1\\ \tan x=-1 \end{array} \right.\Leftrightarrow x=\frac{k\pi}{2}-\frac{\pi}{4}$
6) $pt\Leftrightarrow 2\sin x\cos 2x=\sin x+\sqrt 3\cos 3x$
$\Leftrightarrow \sin 3x-\sqrt 3 \cos 3x=2\sin x$
$\Leftrightarrow -2\cos \left(3x+\frac{\pi}6\right)=2\sin x$
$\Leftrightarrow \cos \left(3x+\frac{\pi}6 \right)=\cos \left( x+\frac{\pi}{2}\right)$