Question

Given that sec0=-37/12, what is the value of cot0, for pi/2<0

Answer 1

Answer:

2nd option

Step-by-step explanation:

Using the identities

tan²θ + 1 = sec²θ

cotθ = $\frac{1}{tan0}$

Given

secθ = - $\frac{37}{12}$ , then

tan²θ + 1 = (- $\frac{37}{12}$ )² = $\frac{1369}{144}$ ( subtract 1 from both sides )

tan²θ = $\frac{1225}{144}$ ( take the square root of both sides )

Since $\frac{\pi }{2}$ < θ < π and tanθ < 0 , then

tanθ = - $\frac{35}{12}$

Then

cotθ = $\frac{1}{-\frac{35}{12} }$ = - $\frac{12}{35}$