Đáp án:
D
Giải thích các bước giải:
\(\begin{array}{l}
\tan \dfrac{a}{2} = 2\\
\to \sin \dfrac{a}{2} = 2\cos \dfrac{a}{2}\\
{\sin ^2}\dfrac{a}{2} + {\cos ^2}\dfrac{a}{2} = 1\\
\to 4{\cos ^2}\dfrac{a}{2} + {\cos ^2}\dfrac{a}{2} = 1\\
\to {\cos ^2}\dfrac{a}{2} = \dfrac{1}{5}\\
B = \dfrac{{1 + 5\cos a}}{{3 - 2\cos a}} = \dfrac{{1 + 5.\left( {2{{\cos }^2}\dfrac{a}{2} - 1} \right)}}{{3 - 2\left( {2{{\cos }^2}\dfrac{a}{2} - 1} \right)}}\\
= \dfrac{{1 + 5.\left( {2.\dfrac{1}{5} - 1} \right)}}{{3 - 2\left( {2.\dfrac{1}{5} - 1} \right)}} = - \dfrac{{10}}{{21}}\\
\to D
\end{array}\)
