Đáp án:
\(G = \dfrac{{205}}{{36}}\)
Giải thích các bước giải:
\(\begin{array}{l}
Do:x \in \left( {\dfrac{\pi }{2};\pi } \right)\\
\to \left\{ \begin{array}{l}
\cos x < 0\\
\sin x > 0
\end{array} \right.\\
Có:{\sin ^2}x + {\cos ^2}x = 1\\
\to {\sin ^2}x + {\left( { - \dfrac{4}{5}} \right)^2} = 1\\
\to {\sin ^2}x = \dfrac{9}{{25}}\\
\to \sin x = \dfrac{3}{5}\\
\to \tan x = \dfrac{{\sin x}}{{\cos x}} = - \dfrac{3}{4}\\
\to \cot x = - \dfrac{4}{3}\\
G = - 3\tan x - \cot x + \dfrac{{\sin x}}{{1 + \cos x}}\\
= - 3.\left( { - \dfrac{3}{4}} \right) - \left( { - \dfrac{4}{3}} \right) + \dfrac{3}{5}:\left( {1 - \dfrac{4}{5}} \right) = \dfrac{{205}}{{36}}
\end{array}\)
