Answer
a. $y=tan(2x)$
b. see explanations.
Work Step by Step
a. It appears that the function $y=tan(2x)$ gives the same graph.
b. Using the sum to product formula, we have
$cos(x)-cos(5x)=-2sin(\frac{x+5x}{2}) sin(\frac{x-5x}{2})=2sin(3x) sin(2x)$ and $sin(x)+sin(5x)=2sin(\frac{x+5x}{2}) cos(\frac{x-5x}{2})=2sin(3x) cos(2x)$
Thus we have
$y=\frac{cos(x)-cos(5x)}{sin(x)+sin(5x)}=\frac{2sin(3x) sin(2x)}{2sin(3x) cos(2x)}=tan(2x)$
