Question

Give. COT A THE following is in the photo below

Answer 1

Answer:
`\sec A=\frac{3\sqrt[]{1521}}{22}`

Step-by-step explanation:

Given that

`\cot A=-\frac{2}{\sqrt[]{117}}`

Since

`\begin{gathered} \cot A=(1)/(\tan A) \\ \\ We\text{ have} \\ (1)/(\tan A)=-\frac{2}{\sqrt[]{117}} \\ \\ \tan A=-\frac{\sqrt[]{117}}{2} \\ \\ (\sin A)/(\cos A)=-\frac{\sqrt[]{117}}{2} \end{gathered}`

Note that:

`\sec A=(1)/(\cos A)`

So,

`\begin{gathered} A=\cot ^(-1)(-\frac{2}{\sqrt[]{117}}) \\ \\ \sin A=\sin (\cot ^(-1)(-\frac{2}{\sqrt[]{117}})) \end{gathered}`

`\begin{gathered} \sec A=-\frac{\sqrt[]{117}}{2}\sin A \\ \\ =-\frac{\sqrt[]{117}}{2}*-\frac{3\sqrt[]{13}}{11} \\ \\ =\frac{3\sqrt[]{1521}}{22} \end{gathered}`