Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{\pi }{2} < a < \pi \Rightarrow \left\{ \begin{array}{l}
\sin a > 0\\
\cos a < 0
\end{array} \right.\\
{\sin ^2}a + {\cos ^2}a = 1\\
\Leftrightarrow {\left( {\dfrac{3}{4}} \right)^2} + {\cos ^2}a = 1\\
\Leftrightarrow {\cos ^2}a = \dfrac{7}{{16}}\\
\cos a < 0 \Rightarrow \cos a = - \dfrac{{\sqrt 7 }}{4}\\
\sin 2a = 2\sin a.\cos a = 2.\dfrac{3}{4}.\left( { - \dfrac{{\sqrt 7 }}{4}} \right) = \dfrac{{ - 3\sqrt 7 }}{8}\\
\cos 2a = 2{\cos ^2}a - 1 = 2.{\left( { - \dfrac{{\sqrt 7 }}{4}} \right)^2} - 1 = - \dfrac{1}{8}\\
\tan 2a = \dfrac{{\sin 2a}}{{\cos 2a}} = 3\sqrt 7
\end{array}\)
