Question 973828
<pre> 
Remember the identity: {{{sin^2(theta)+cos^2(theta)=1}}}?
Subtract {{{cos^2(theta)}}} from both sides and get {{{sin^2(theta)=1-cos^2(theta)}}}  

The right side of that shows that the denominator of what you have so far
is {{{sin^2(x)}}}

{{{2cos(x)/(1-cos^2(x))}}} becomes:

{{{2cos(x)/sin^2(x)}}}

Change the choices to all sines and cosines until you find
which one is equivalent.  Begin with A)

A) 2cot(x)csc(x)

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

{{{2cos(x)/sin^2(x)}}}

So A) happens to be the correct choice.

We were lucky to get it on the first try.  If that had not
been the correct choice we would have changed the others to
sines and cosines, until we found the correct choice.

Edwin</pre>