Find all solutions of each equation on the interval 0 ≤ x < 2π.
tan^2 x sec^2 x + 2sec^2 x - tan^2 x = 2

or .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

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Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, . Therefore, for the square of tangents,

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This equation will thus become:

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To simplify the calculations, replace all with another variable. For example, let . Keep in mind that .

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Solve this equation for :

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Given that , is the only possible solution.

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, where (i.e., is an integer.)

Given that ,

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or . Accordingly,

or .