Answer
a. $cot(x)$
b. see explanations.
Work Step by Step
a. The graph looks like the function $z=cot(x)$
b. Using the Sum-to- Product Formulas, we have
$y=\frac{2cos(\frac{3x+x}{2})cos(\frac{3x-x}{2})}{2cos(\frac{3x+x}{2})sin(\frac{3x-x}{2})}=\frac{cos(2x)cos(x)}{cos(2x)sin(x)}=cot(x)$
Thus functions $y$ and $z$ are equivalent.
