[tex]sec x - tan x = \frac{1}{4} \\\\ sec x = tan x + \frac{1}{4} \\\\ sec x = \frac{4tan x + 1}{4} \\\\ sec x + tan x = y \\\ \frac{4tan x + 1}{4} + tan x = y \\\\ \frac{4tan x + 1 + 4tan x}{4} = y \\\\ \frac{8tan x + 1}{4} = y \\\\ y = 2tan x + \frac{1}{4}[/tex]
