How do you factor the expression and use the fundamental identities to simplify #csc^3x-csc^2x-cscx+1#?

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Answer 1 · 2017-03-28T17:26:11

#x=pm pi/2+2kpi# with #k in ZZ#

Considering #y = cscx#

#y^3-y^2-y+1=0# has a root for #y = 1#

and

#y^3-y^2-y+1=(y^2-1)(y-1)#

or

#y^3-y^2-y+1=(y+1)(y-1)^2# so the solutions are

#cscx=pm1# or

#sinx=pm1#

or

#x=pm pi/2+2kpi# with #k in ZZ#