$\dfrac{\pi}{2}<\alpha<\pi$
$\to \sin\alpha>0, \cos\alpha<0$
$\to \cos\alpha=-\sqrt{1-\sin^2\alpha}=-\sqrt{ 1-\Big( \dfrac{3}{4}\Big)^2}=\dfrac{-\sqrt7}{4}$
$\to \tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{-3\sqrt7}{7}$
$\to \cot\alpha=\dfrac{1}{\tan\alpha}=\dfrac{-\sqrt7}{3}$
$E=\dfrac{ 2\tan\alpha-3\cot\alpha}{\cos\alpha+\tan\alpha}=\dfrac{ -2.\dfrac{3\sqrt7}{7}+3.\dfrac{\sqrt7}{3} }{ \dfrac{-\sqrt7}{4}-\dfrac{3\sqrt7}{7}}=\dfrac{-4}{19}$
$F=\dfrac{\cos^2\alpha+\cot^2\alpha}{\tan\alpha-\cot\alpha}=\dfrac{ \Big( \dfrac{-\sqrt7}{4}\Big)^2+\Big( \dfrac{-\sqrt7}{3}\Big)^2 }{ -\dfrac{3}{\sqrt7}+\dfrac{\sqrt7}{3}}=\dfrac{175}{144}: \dfrac{-2\sqrt7}{21}=\dfrac{-1225}{96\sqrt7}$
