\(\begin{array}{l}
14)\,\\
pt\, \Leftrightarrow 4\cos x = \sqrt 2 \left( {1 + {{\tan }^2}x} \right)\,\,\,\left( {\cos x \ne 0} \right)\\
\Leftrightarrow 4\cos x = \sqrt 2 .\dfrac{1}{{{{\cos }^2}x}}\\
\Leftrightarrow {\cos ^3}x = \dfrac{1}{{2\sqrt 2 }}\\
\Leftrightarrow \cos x = \dfrac{1}{{\sqrt 2 }} \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{4} + k2\pi \\
x = - \dfrac{\pi }{4} + k2\pi
\end{array} \right.
\end{array}\)
