Answer:[tex]\sec A=\frac{3\sqrt[]{1521}}{22}[/tex]
Explanation:
Given that
[tex]\cot A=-\frac{2}{\sqrt[]{117}}[/tex]
Since
[tex]\begin{gathered} \cot A=\frac{1}{\tan A} \\ \\ We\text{ have} \\ \frac{1}{\tan A}=-\frac{2}{\sqrt[]{117}} \\ \\ \tan A=-\frac{\sqrt[]{117}}{2} \\ \\ \frac{\sin A}{\cos A}=-\frac{\sqrt[]{117}}{2} \end{gathered}[/tex]
Note that:
[tex]\sec A=\frac{1}{\cos A}[/tex]
So,
[tex]\begin{gathered} A=\cot ^{-1}(-\frac{2}{\sqrt[]{117}}) \\ \\ \sin A=\sin (\cot ^{-1}(-\frac{2}{\sqrt[]{117}})) \end{gathered}[/tex]
[tex]\begin{gathered} \sec A=-\frac{\sqrt[]{117}}{2}\sin A \\ \\ =-\frac{\sqrt[]{117}}{2}\times-\frac{3\sqrt[]{13}}{11} \\ \\ =\frac{3\sqrt[]{1521}}{22} \end{gathered}[/tex]
