Question 1205700
<pre>
{{{(cot(x) + csc(x) -1)/(cot(x) - csc(x) +1) = csc(x) + cot(x)}}}

{{{(cos(x)/sin(x) + 1/sin(x) -1)/(cos(x)/sin(x) - 1/sin(x) +1)}}}

Replace the trig ratios cos(x) and sin(x) by their initials C and S:

{{{(C/S + 1/S -1)/(C/S - 1/S +1)}}}

{{{(C + 1 -S)/(C - 1 +S)}}}

{{{((C-S)+1)/((C+S)-1)}}}

{{{((C-S)+1)/((C+S)-1)}}}{{{""*""}}}{{{((C+S)+1)/((C+S)+1)}}}

{{{(  (C-S) (C+S)+1(C-S)+1(C+S)+1)/((C+S)^2-1)}}}

{{{(C^2-S^2+C-S+C+S+1)/(C^2+2CS+S^2-1)}}}

{{{(C^2-S^2+2C+1)/((C^2+S^2)+2CS-1)}}}

Since {{{cos^2(x)+sin^2(x)=1}}}, Replace the 1 in the top by
{{{C^2+S^2}}} and vice versa in the bottom:

{{{(C^2-S^2+2C+C^2+S^2)/(1+2CS-1)}}}

{{{(2C^2+2C)/(2CS^"")}}}

{{{(2C^2)/(2CS^"")+(2C^"")/(2CS^"")}}}

{{{C/S+1/S}}}

{{{cos(x)/sin(x)+1/sin(x)}}}

{{{cot(x)+csc(x)}}}

{{{csc(x)+cot(x)}}}

Whew!

Edwin</pre>