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.
Let . Substitute for all occurrences of .
Factor using the perfect square rule.
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 .
Set the factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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