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
$sin(x)-sin(3x)=2cos(\frac{x+3x}{2})sin(\frac{x-3x}{2})=-2cos(2x) sin(x)$
and
$cos(x)-cos(3x)=-2sin(\frac{x+3x}{2}) sin(\frac{x-3x}{2})=2sin(2x) sin(x)$
Thus we have
$y=\frac{sin(x)-sin(3x)}{cos(x)-cos(3x)}=\frac{-2cos(2x) sin(x)}{2sin(2x) sin(x)}=-cot(2x)$
