Question #18917

1 Answer
Nghi N.
Feb 8, 2017

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

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