Step-by-step explanation:
[tex] {EF}^{2} = {EG}^{2} - {FG}^{2} \\ \\ = {8}^{2} - {6}^{2} \\ \\ = 64 - 36 \\ \\ = 28 \\ \\ \therefore \: {EF} = \sqrt{28} \\ \\ \therefore \: {EF} = 2\sqrt{7} \\ \\
\sin \: E = \frac{FG }{EG} = \frac{6}{8} = \frac{3}{4} \\ \\ \huge\red {\boxed{\therefore \: \sin \: E = \frac{3}{4}} } \\
\sec \: G = \frac{ EG}{FG} = \frac{8}{6} = \frac{4}{3} \\ \\ \huge\purple {\boxed{ \therefore \: \sec \: G = \frac{4}{3}}} \\\\
\cot \: G = \frac{ FG}{EF} = \frac{6}{2\sqrt 7} = \frac{3}{\sqrt 7} \\ \\ = \frac{3\times\sqrt 7 }{\sqrt 7\times\sqrt 7 } \\ \\ = \frac{3\sqrt 7 }{ 7 } \\ \\
\huge\orange {\boxed{ \therefore \: \cot \: G = \frac{3\sqrt 7 }{ 7 } }} \\\\ [/tex]
