SOLUTION: please help me factor & simplify: csc^3x-csc^2x-cscx+1

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Question 622080: please help me factor & simplify:
csc^3x-csc^2x-cscx+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z = cscx

csc^3x-csc^2x-cscx+1

z^3-z^2-z+1

(z^3-z^2)+(-z+1)

z^2(z-1)+(-z+1)

z^2(z-1)-1(z-1)

(z^2-1)(z-1)

(z-1)(z+1)(z-1)

(z+1)(z-1)(z-1)

(z+1)(z-1)^2

(cscx+1)(cscx-1)^2

So csc^3x-csc^2x-cscx+1 completely factors to (cscx+1)(cscx-1)^2