Textbook Problem

In Exercises 33 to36, 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 $\alpha \ne {90}^{\circ }$, prove the identity $\tan \alpha =\frac{\sin \alpha }{\cos \alpha }$

(HINT: $\sin \alpha =\frac{a}{c}$ and $\cos \alpha =\frac{b}{c}.$)

b) Use your calculator to show that $\tan {23}^{\circ }$ and $\frac{\sin {23}^{\circ }}{\cos {23}^{\circ }}$ are equivalent.