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 .

ratio is 2 : 9

the answer is three

13.5 : 3

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.