Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 194: 25

$$\tan(-\theta)=-\tan\theta$$

From the Negative-Angle Identities, we know that $$\tan(-\theta)=-\tan\theta$$ Therefore, we should fill in the blank with $-\tan\theta$. Actually, if you don't remember this identity, you can yourself make out by using the Quotient Identity: $$\tan(-\theta)=\frac{\sin(-\theta)}{\cos(-\theta)}=\frac{-\sin\theta}{\cos\theta}=-\tan\theta$$