Which shows all the exact solutions of 2sec^2x-tan^4x=-1 ? give your answer in radians.

You can use the fact that the range of tangent function is whole set of real numbers.
The solutions to the given equation are

It is a fact that tangent ratio has range as all real numbers. We can use this fact along with the second Pythagorean identity to get to the solution of the given equation.

The given equation is

Using the second Pythagorean identity, we get the equation as

Assuming , then we get

The equation becomes

As we know that y is non-negative, so only valid solution is y = 3

Thus,

Thus,

Thus, the solutions to the given equation are:

Converting to radians,

Thus,The solutions to the given equation are

Learn more about trigonometric ratios here:

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is means division by fractions

step-by-step explanation:

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step-by-step explanation: