# Solve for x sec(x)^4-tan(x)^4=1+2tan(x)^2

Solve for x sec(x)^4-tan(x)^4=1+2tan(x)^2
Simplify the left side.
Simplify the expression.
Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply pythagorean identity.
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Set up the equation to solve for .
Solve the equation for .
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify the left side of the equation.
Solve for .
Replace the with based on the identity.
Combine the opposite terms in .
Subtract from .
For the two functions to be equal, the arguments of each must be equal.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Since , the equation will always be true.
All real numbers
All real numbers
All real numbers
Set up the equation to solve for .
Solve the equation for .
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify the left side of the equation.
Solve for .
Simplify the left side.
Rearrange terms.
Apply pythagorean identity.
Simplify the expression.
Raise to the power of .
Multiply by .
For the two functions to be equal, the arguments of each must be equal.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Since , the equation will always be true.
All real numbers
All real numbers
All real numbers
The complete solution is the set of all solutions.
No solution
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