\(cosx=\sqrt{1-\dfrac{7}{16}}=\dfrac{3}{4}\)
\(tanx=\dfrac{\sqrt{7}}{4}:\dfrac{3}{4}=\dfrac{\sqrt{7}}{3}\)
\(cotx=1:\dfrac{\sqrt{7}}{3}=\dfrac{3}{\sqrt{7}}=\dfrac{3\sqrt{7}}{7}\)
\(M=\left(\dfrac{3}{7}\sqrt{7}+\dfrac{1}{3}\sqrt{7}\right):\left(\dfrac{3}{7}\sqrt{7}-\dfrac{1}{3}\sqrt{7}\right)\)
\(=\dfrac{16}{21}:\dfrac{2}{21}=8\)