Help with solving this equation

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To solve the equation (sec x)^2 (tan x)^2 = 2, it can be rewritten using the identity (sec x)^2 = 1 + (tan x)^2. This leads to the equation (tan x)^2 + (tan x)^4 - 2 = 0. By substituting "u = tan x," the problem can be transformed into a quadratic equation. This substitution simplifies the solving process, allowing for easier manipulation of the terms. The next step is to solve the resulting quadratic equation for u.
donjt81
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Hi guys

I was solving a problem and I am stuck at solving this equation.

(sec x)^2 (tan x)^2 = 2
since we know that (sec x)^2 = 1 + (tan x)^2

[1 + (tan x)^2][(tan x)^2] = 2
(tan x)^2 + (tan x)^4 - 2 = 0

now what do i do...

thanks in advance.
 
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Substitute "u = tan x" to get a quadratic.
 

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