Solve for x in Degrees 2sin(x)tan(x)+tan(x)=0

Solve for x in Degrees 2sin(x)tan(x)+tan(x)=0
Simplify the left side of the equation.
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Simplify each term.
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Rewrite in terms of sines and cosines.
Multiply .
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Combine and .
Combine and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite in terms of sines and cosines.
Simplify each term.
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Factor out of .
Separate fractions.
Convert from to .
Divide by .
Convert from to .
Factor out of .
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Factor out of .
Raise to the power 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 .
Solve for .
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Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Add and .
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 degrees 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.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Move the negative in front of the fraction.
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees 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 and to .
, for any integer
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Name

Name two billion seventy-two million two hundred thirty-nine thousand eight hundred eighty-four

Interesting facts

  • 2072239884 has 64 divisors, whose sum is 5089996800
  • The reverse of 2072239884 is 4889322702
  • Previous prime number is 383

Basic properties

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

Name

Name eight hundred forty-seven million three hundred thirty-seven thousand one hundred eighty-eight

Interesting facts

  • 847337188 has 64 divisors, whose sum is 2077498368
  • The reverse of 847337188 is 881733748
  • Previous prime number is 197

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 49
  • Digital Root 4

Name

Name six hundred fifty-seven million two hundred ninety-one thousand two hundred one

Interesting facts

  • 657291201 has 4 divisors, whose sum is 688590804
  • The reverse of 657291201 is 102192756
  • Previous prime number is 21

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 33
  • Digital Root 6