Đáp án:
\(x = \arctan \left( {1,167327637} \right) + k\pi \)
Giải thích các bước giải:
\(\begin{array}{l}
DK:\left\{ \begin{array}{l}
\sin x \ne 0\\
\cos x \ne 0
\end{array} \right. \to \sin 2x \ne 0\\
\to 2x \ne k\pi \to x \ne \dfrac{{k\pi }}{2}\\
5{\cot ^2}x - 4\tan x + 1 = 0\\
\to \dfrac{5}{{{{\tan }^2}x}} - 4\tan x + 1 = 0\\
\to - 4{\tan ^3}x + {\tan ^2}x + 5 = 0\\
\to \tan x = 1,167327637\\
\to x = \arctan \left( {1,167327637} \right) + k\pi \left( {k \in Z} \right)
\end{array}\)
