Question

Question #18917

Answer 1

sec x

Explanation:

`f(x) = cos x/(1 - sin x) - sin x/(cos x) =`
`= [cos^2 x - sin x(1 - sin x)]/(cos x(1 - sin x))`
The numerator results in:
`(cos^2 x - sin x + sin^2 x) = 1 - sin x`,
because `sin^2 x + cos^2 x = 1`
Finally,
`f(x) = (1- sin x)/(cos x(1 - sin x)) = 1/(cos x) = sec x`