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

Lets solve the trigonometric equation 

Step 1. Use the trigonometric identity: :



Step 2. Subtract 1 from both sides of the equation:



Step 3. Substitute :


Step 3. Multiply both sides of the equation by -1:



Step 4. Solve for :


Step 5. Substitute :


Step 6. Solve for :


Since  is not a real root, we can rule out 




We can conclude that the exact solution of the equation are  and , which are approximately  and  respectively. 

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

What are Pythagorean identities ?

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:

link

I'm pretty sure it's b). i try drawing the functions out and b is the one that stands out or isnt a "line"

7.666270253x10 raised to the 18th power