Question

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

Answer 1

2nd option

Explanation:

Using the identities

tan²θ + 1 = sec²θ

cotθ =
`(1)/(tan0)`

Given

secθ = -
`(37)/(12)` , then

tan²θ + 1 = (-
`(37)/(12)` )² =
`(1369)/(144)` ( subtract 1 from both sides )

tan²θ =
`(1225)/(144)` ( take the square root of both sides )

Since
`(\pi )/(2)` < θ < π and tanθ < 0 , then

tanθ = -
`(35)/(12)`

Then

cotθ =
`(1)/(-(35)/(12) )` = -
`(12)/(35)`