Question

How do you find the exact value of `sec(u+v)` given that `sinu=-7/25` and `cosv=-4/5`?

Answer 1

Many possible answers.

Explanation:

First evaluate cos (u + v) by trig identity:
cos ( u + v) = cos u.cos v - sin u.sin v
Find cos u and sin u.
`sin u = - 7/25` --> `cos^2 u = 1 - 49/625 = 576/625` -->
`cos u = +- 24/25`
#cos v = -4/5 --> sin^2 v = 1 - 16/25 = 9/25 --> #sin v = +- 3/5#
The problem leads to many possible answers, depending on the location of u and v in the unit circle.
The locations of u and v, in any Quadrant, should be given in order to compute the answer.