Answer
a. $y=-cot(2x)$
b. See explanations.
Work Step by Step
a. It appears that the function $y=cot(2x)$ gives the same graph.
b. Using the sum to product formula, we have
$sin(2x)+sin(6x)=2sin(\frac{2x+6x}{2})cos(\frac{2x-6x}{2})=2sin(4x) cos(2x)$
and
$cos(6x)-cos(2x)=-2sin(\frac{6x+2x}{2}) sin(\frac{6x-2x}{2})=-2sin(4x) sin(2x)$
Thus we have
$y=\frac{sin(2x)+sin(6x)}{cos(6x)-cos(2x)}=\frac{2sin(4x) cos(2x)}{-2sin(4x) sin(2x)}=-cot(2x)$
