Finding cosx/(1 - 5sin x) given a constraint on cos²x and sin²x

[wei1006]

1) Problem: given that x is an obtuse angle for which cos^2x/(1 + 5sin^2x) = 8/35, find the value of cosx/(1 - 5 sin x) without evaluating x.

2) relevant equations:
sin(-x) = - sin x
cos(-x) = cos x
sin(180° - x) = sin x
cos(180° - x) = - cos x
sin^2x + cos^2x = 1

3) Attempt:
cos^2x/(1 + 5sin^2x) = 8/35
35cos^2x = 8 + 40sin^2x

Actually I am clueless on how to tackle this problem, as in what should I be even doing to get to the answer.

Please help, thank you!

 

[haruspex]

Try combining the last of your 'relevant equations' with the last equation in your attempt.