Textbook Problem

In Exercises 33 to 36, we expand the list of trigonometric identities. As you may recall, an identity is a statement that is true for all permissible choices of the variable (see page 502.)

a) For $\alpha \ne 0^{\circ }$, prove the identity $\cot \alpha =\frac{\cos \alpha }{\sin \alpha }.$

b) Use your calculator to determine $\cot {57}^{\circ }$ by dividing $\cos {57}^{\circ }$ by $\sin {57}^{\circ }.$