Question

simplify using fundamental identities
csc^3x-csc^2x-cxcx+1

Answer 1

Ouch. The usage of letters instead of the ratios makes it look confusing but this is the identity right? :
\[\csc^3x-\csc^2x-\csc x+1\]

Answer 2

yes

Answer 3

take csc^2 and -1 common factors leading to

\[\csc ^2(x)[\csc(x) - 1] -1[\csc (x) -1] \]

leading to:

\[(\csc ^2(x) -1) (\csc (x) -1)\]