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.
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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 .
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Set equal to .
Solve for .
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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.
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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 .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Find the period of .
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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 .
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Set equal to .
Solve for .
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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.
Tap for more steps...
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 .
Tap for more steps...
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
Consolidate the answers.
, for any integer
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Name

Name one billion six hundred thirty-nine million six hundred forty-one thousand seventy-one

Interesting facts

  • 1639641071 has 8 divisors, whose sum is 1663683840
  • The reverse of 1639641071 is 1701469361
  • Previous prime number is 137

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2

Name

Name one billion seven hundred fifty million five hundred thousand eight hundred ninety-seven

Interesting facts

  • 1750500897 has 32 divisors, whose sum is 2505613824
  • The reverse of 1750500897 is 7980050571
  • Previous prime number is 821

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name one billion six hundred seventy-six million five hundred ninety-four thousand nine hundred one

Interesting facts

  • 1676594901 has 4 divisors, whose sum is 2235459872
  • The reverse of 1676594901 is 1094956761
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3