# 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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