b.
In order to calculate the cotangent of 60°, we can use the relation below:
[tex]\cot (90\degree-x)=\frac{1}{\cot x}=\frac{1}{\frac{1}{\tan x}}=\tan x[/tex]So we have:
[tex]\begin{gathered} \cot (90\degree-30\degree)=\frac{1}{\cot (30\degree)} \\ \cot (60\degree)=\frac{1}{\frac{1}{\tan30\degree}}=\tan 30\degree \\ \cot (60\degree)=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]c.
To calculate the cosine of 30°, we can use the relation below:
[tex]\tan x=\frac{\sin x}{\cos x}[/tex]So we have:
[tex]\begin{gathered} \tan 30=\frac{\sin 30}{\cos 30} \\ \frac{\sqrt[]{3}}{3}=\frac{\frac{1}{2}}{\cos 30} \\ \sqrt[]{3}\cos 30=\frac{3}{2} \\ \cos 30=\frac{3}{2\sqrt[]{3}}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]d.
Calculating the cotangent of 30°, we have:
[tex]\cot (30\degree)=\frac{1}{\tan(30\degree)}=\frac{1}{\frac{\sqrt[]{3}}{3}}=\frac{3}{\sqrt[]{3}}=\sqrt[]{3}[/tex]