# Solve for x in Radians sec(x)^2-sec(x)=2

Solve for x in Radians sec(x)^2-sec(x)=2
Subtract from both sides of the equation.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Add to both sides of the equation.
Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
The exact value of is .
The secant function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
The exact value of is .
The secant function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Subtract from .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
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### Name

Name one billion five hundred sixty-five million two hundred forty-five thousand nine hundred fifty-three

### Interesting facts

• 1565245953 has 8 divisors, whose sum is 2782659488
• The reverse of 1565245953 is 3595425651
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 45
• Digital Root 9

### Name

Name six hundred ten million one hundred seventy-six thousand seven hundred thirty-six

### Interesting facts

• 610176736 has 128 divisors, whose sum is 4989958344
• The reverse of 610176736 is 637671016
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1

### Name

Name one billion seven hundred thirty-five million seventy-three thousand six hundred thirty-nine

### Interesting facts

• 1735073639 has 8 divisors, whose sum is 1869263760
• The reverse of 1735073639 is 9363705371
• Previous prime number is 48907

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 44
• Digital Root 8