Answer:
2nd option
Step-by-step explanation:
Using the identities
tan²θ + 1 = sec²θ
cotθ = [tex]\frac{1}{tan0}[/tex]
Given
secθ = - [tex]\frac{37}{12}[/tex] , then
tan²θ + 1 = (- [tex]\frac{37}{12}[/tex] )² = [tex]\frac{1369}{144}[/tex] ( subtract 1 from both sides )
tan²θ = [tex]\frac{1225}{144}[/tex] ( take the square root of both sides )
Since [tex]\frac{\pi }{2}[/tex] < θ < π and tanθ < 0 , then
tanθ = - [tex]\frac{35}{12}[/tex]
Then
cotθ = [tex]\frac{1}{-\frac{35}{12} }[/tex] = - [tex]\frac{12}{35}[/tex]
