Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 682: 101

See graph. a. $y=tan(\frac{x}{2})$ b. See explanations.

Graph the equation as shown in the figure. a. The graph appears to be the same as $y=tan(\frac{x}{2})$ b. Using the double angle formulas, we have $y=csc(x)-cot(x)=\frac{1}{sin(x)}-\frac{cos(x)}{sin(x)}=\frac{1-cos(x)}{sin(x)}=\frac{1-(1-2sin^2(x/2))}{2sin(x/2)cos(x/2)}=tan(\frac{x}{2})$