SOLUTION: Prove the identity: {{{csc(x)+cot(x)=sin(x)/(1-cos(x))}}}

Replace  on left side by 
Replace  on left side by 



Combine the numerators over the common denominator:



Form the conjugate of the numerator by changing the sign
of the second term:  , put it over itself,
like this , which equals 1,
so we can multiply by it without changing the value:



Indicate the multiplications of the tops and bottoms:



FOIL out the top:



Simplify by canceling in the top:





Replace  by 



The  in the bottom cancels out the
square in the top:





Edwin