# 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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### Name

Name one billion one hundred seventy-six million two hundred fifty-nine thousand eight hundred seventy-five

### Interesting facts

• 1176259875 has 32 divisors, whose sum is 1910599680
• The reverse of 1176259875 is 5789526711
• Previous prime number is 109

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 51
• Digital Root 6

### Name

Name three hundred fifty-six million two hundred twenty thousand five hundred seventy-eight

### Interesting facts

• 356220578 has 8 divisors, whose sum is 610663872
• The reverse of 356220578 is 875022653
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name one billion three hundred seventeen million four hundred sixty-one thousand one hundred sixty-five

### Interesting facts

• 1317461165 has 8 divisors, whose sum is 1582639128
• The reverse of 1317461165 is 5611647131
• Previous prime number is 941

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8