Rewrite each expression in terms of one trigonometric function.  

1. $\frac { 1 + \operatorname { cos } ( 2 x ) } { \operatorname { sin } ( 2 x ) }$ 

   Step (a):

   $\frac{1+1-2\sin^2(x)}{2\sin(x)\cos(x)}$

2. $\cos^2( \frac { x } { 4 } )− \sin^2( \frac { x } { 4 } )$ 

   Hint (b):

   Review the double-angle identities for cosine.

3. $(1+\cot2(y))(\cos(2y)+1)$ 

   Step 1(c):

   $(1+\cot^2(y))(\cos^2(y)-\sin^2(y)+1)$

   Step 2(c):

   $\left(1+\frac{\cos^2(y)}{\sin^2(y)}\right)(2\cos^2(y))$