Question

sec x tan x / sec x - tan x
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Answer 1

Let y = (sec x + tan x)/(sec x – tan x)

= (1+ sin x)/(1-sin x)

Use quotient rule and differentiate w.r.t.x

dy/dx = [(1-sin x) cos x + (1+sin x) cos x]/(1-sin x)2

= [cos x – sin x cos x + cos x + sin x cos x]/(1-sin x)2

= 2 cos x/(1-sin x)2