How to solve: csc(x)^2 -2(csc x) + 4csc(x) = 2?

Question

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Answer 1

csc(x)^2 -2(csc x) + 4csc(x) = 2? I did some corrections?
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csc(x)^2 - 2csc (x) + 4csc(x) = 2 I did some corrections?
Or cosc^2(x) + 2cosc(x) -2 =0.
Put cosc(x) = y, the above equations becomes : y^2 +2y -2-0.
Its roots are: y=(1/2)[ -2 + or - sqrt(4+8)] Or
=(1/2)[ -2 + or - 2 sqrt(2)] or
= -1 + or - sqrt(2)
= sqrt(2) -1 Or -(sqrt(2) +1)
Or sin(x) =1/[sqrt(2) -1] or -1/ [sqrt(2) +1]
The first root > 1 and so is not acceptable.
So: sin x = - 0.4142.= - sin(0.136 pi)
Hence x = pi +0.136 pi or 2pi -0.136 pi
= 1.136 pi or 1.864 pi Answer.

Answer 2

csc(x)^2 -2(csc x) + 4csc(x) = 2
csc^2 x + 2csc x -2 = 0
csc x = [-2 +/- sqrt(4-4(-4))]/2
csc x = -1 +/- sqrt(5)
1/sin x = -1+/- sqrt(5)
sin x 1/(-1+/- sqrt(5)
x = arc sin [1/(-1-sqrt(5))] = -18 degrees
x = arcsin [1/(-1+sqrt(5))] = 54 degrees

Answer 3

csc^2(x) - 2csc(x) + 4csc(x) = 2

Group like terms.

csc^2(x) + 2csc(x) = 2

csc^2(x) + 2csc(x) - 2 = 0

Are you sure you wrote the question down correctly? It doesn't work out to a pretty answer.