Đáp án:
sinx=1
Giải thích các bước giải:
\(\begin{array}{l}
Do:x \in \left( {\dfrac{\pi }{2};\pi } \right)\\
\to \left\{ \begin{array}{l}
\cos x < 0\\
\sin x > 0
\end{array} \right.\\
Do:\sin x + \cos x = \dfrac{1}{5}\\
\to \sin x = \dfrac{1}{5} - \cos x\\
{\sin ^2}x + {\cos ^2}x = 1\\
\to \dfrac{1}{{25}} + \dfrac{2}{5}\cos x + {\cos ^2}x + {\cos ^2}x = 1\\
\to 2{\cos ^2}x + \dfrac{2}{5}\cos x - \dfrac{{24}}{{25}} = 0\\
\to \left[ \begin{array}{l}
\cos x = \dfrac{3}{5}\left( l \right)\\
\cos x = - \dfrac{4}{5}\left( {TM} \right)
\end{array} \right.\\
\to \sin x = 1\\
\tan x = - \dfrac{5}{4}\\
\cot x = - \dfrac{4}{5}
\end{array}\)
