Solve for x 4csc(x)^2+4csc(x)+1=0

Solve for x 4csc(x)^2+4csc(x)+1=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor using the perfect square rule.
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Rewrite as .
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Replace all occurrences of with .
Replace the left side with the factored expression.
Set equal to and solve for .
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Set the factor equal to .
Subtract from both sides of the equation.
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 .
Move the negative in front of the fraction.
The range of cosecant is and . Since does not fall in this range, there is no solution.
No solution
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Name

Name two billion eighty-one million two hundred five thousand eleven

Interesting facts

  • 2081205011 has 4 divisors, whose sum is 2081897400
  • The reverse of 2081205011 is 1105021802
  • Previous prime number is 3019

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 20
  • Digital Root 2

Name

Name one billion seven hundred sixteen million seven hundred sixty-three thousand fifty

Interesting facts

  • 1716763050 has 16 divisors, whose sum is 2591256000
  • The reverse of 1716763050 is 0503676171
  • Previous prime number is 199

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9

Name

Name sixty-nine million two hundred sixty thousand four hundred ninety-three

Interesting facts

  • 69260493 has 8 divisors, whose sum is 92914528
  • The reverse of 69260493 is 39406296
  • Previous prime number is 163

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 39
  • Digital Root 3