Verify the identity 1/secx-tanx=secx+tanx .

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You need to transform both sides expanding the function sec x into fraction such that:

`1/(1/(cos x) - tan x) = 1/(cos x)+ tan x`

Cross multiplying yields:

`1 = (1/(cos x) - tan x)(1/(cos x)+ tan x)`

You may transform the special product to the right in difference of squares...

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You need to transform both sides expanding the function sec x into fraction such that:

`1/(1/(cos x) - tan x) = 1/(cos x)+ tan x`

Cross multiplying yields:

`1 = (1/(cos x) - tan x)(1/(cos x)+ tan x)`

You may transform the special product to the right in difference of squares such that:

`1 = 1/(cos^2 x) - tan^2 x`

This last line expresses one of the three forms of basic trigonometric identity, hence the identity `1/(sec x-tan x)=sec x+tan x`  is established.

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