Solve for x 3sec(x)^2-3=0

Solve for x 3sec(x)^2-3=0
Simplify the left side.
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Simplify with factoring out.
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Factor out of .
Factor out of .
Factor out of .
Apply pythagorean identity.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
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.
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Simplify the right side of the equation.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Add and .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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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
Consolidate the answers.
, for any integer
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Name

Name one billion six hundred fifty-six million sixty-seven thousand eight hundred forty-eight

Interesting facts

  • 1656067848 has 32 divisors, whose sum is 7452305424
  • The reverse of 1656067848 is 8487606561
  • Previous prime number is 3

Basic properties

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

Name

Name one billion five hundred ninety-one million forty-eight thousand three hundred seventy-five

Interesting facts

  • 1591048375 has 32 divisors, whose sum is 1916006400
  • The reverse of 1591048375 is 5738401951
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7

Name

Name six hundred forty-three million one hundred sixty-six thousand five hundred eighty-four

Interesting facts

  • 643166584 has 16 divisors, whose sum is 2170687248
  • The reverse of 643166584 is 485661346
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7