Question 622080
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