Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the trigonometric identity
cot x = [tex]\frac{1}{tanx}[/tex]
Consider tan([tex]\frac{7\pi }{6}[/tex] )
[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant where tan > 0
Thus tan([tex]\frac{7\pi }{6}[/tex] ) = tan([tex]\frac{7\pi }{6}[/tex] - π ) = tan([tex]\frac{\pi }{6}[/tex] ) = [tex]\frac{1}{\sqrt{3} }[/tex]
Hence
cot([tex]\frac{7\pi }{6}[/tex] ) = [tex]\frac{1}{\frac{1}{\sqrt{3} } }[/tex] = [tex]\sqrt{3}[/tex]
