Solve for x in Radians tan(x)^2=sec(x)-1

Solve for x in Radians tan(x)^2=sec(x)-1
Move all the expressions to the left side of the equation.
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Subtract from both sides of the equation.
Add to both sides of the equation.
Simplify the left side of the equation.
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Move .
Apply pythagorean identity.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
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 .
The range of secant is and . Since does not fall in this range, there is no solution.
No solution
No solution
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.
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
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 fifty-eight million six hundred twenty-two thousand four hundred sixty-five

Interesting facts

  • 1058622465 has 16 divisors, whose sum is 1703590848
  • The reverse of 1058622465 is 5642268501
  • Previous prime number is 173

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 39
  • Digital Root 3

Name

Name one billion thirteen million six hundred forty-six thousand four hundred twenty-five

Interesting facts

  • 1013646425 has 16 divisors, whose sum is 1189693440
  • The reverse of 1013646425 is 5246463101
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 32
  • Digital Root 5

Name

Name five hundred twenty-nine million seven hundred seventy-five thousand seven hundred fifty-three

Interesting facts

  • 529775753 has 8 divisors, whose sum is 575578248
  • The reverse of 529775753 is 357577925
  • Previous prime number is 113

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 50
  • Digital Root 5