Question #18917

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Question #18917

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Answer 1 · 2017-02-08T04:57:17

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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Question #18917

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