Solve for x tan(x)^2-1=0

Solve for x tan(x)^2-1=0
Add to both sides of the equation.
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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Any root of is .
The complete solution is the result of both the positive and negative portions of the solution.
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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 .
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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.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
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
, for any integer
Set up the equation to solve for .
Solve the equation for .
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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 negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Simplify .
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Add to .
The resulting angle of is positive and coterminal with .
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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the results found in the previous steps.
, for any integer
The complete solution is the set of all solutions.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name one billion six hundred seventy-seven million forty thousand eighteen

Interesting facts

  • 1677040018 has 8 divisors, whose sum is 2520726912
  • The reverse of 1677040018 is 8100407761
  • Previous prime number is 487

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 34
  • Digital Root 7

Name

Name five hundred twenty-two million nine hundred thirty thousand eight hundred six

Interesting facts

  • 522930806 has 32 divisors, whose sum is 876268800
  • The reverse of 522930806 is 608039225
  • Previous prime number is 59

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion seven hundred two million one hundred thirty thousand one hundred fifteen

Interesting facts

  • 1702130115 has 8 divisors, whose sum is 2334350016
  • The reverse of 1702130115 is 5110312071
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 21
  • Digital Root 3