Answer
a. $y=-tan(x)$
b. See explanations.
Work Step by Step
a. It appears that the function $y=-tan(x)$ gives the same graph.
b. Using the sum to product formula, we have
$cos(5x)-cos(3x)=-2sin(\frac{5x+3x}{2}) sin(\frac{5x-3x}{2})=-2sin(4x) sin(x)$
and
$sin(5x)+sin(3x)=2sin(\frac{5x+3x}{2}) cos(\frac{5x-3x}{2})=2sin(4x) cos(x)$.
Thus we have
$y=\frac{cos(5x)-cos(3x)}{sin(5x)+sin(3x)}=\frac{-2sin(4x) sin(x)}{2sin(4x) cos(x)}=-tan(x)$
