5. If $\sin \theta+\cos \theta=\frac{6}{5}$, evaluate $\tan \theta+\cot \theta$.
Answer: $\frac{50}{11}$
Solution: We have
$$
\tan \theta+\cot \theta=\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}=\frac{1}{\sin \theta \cos \theta} .
$$

Thus, since $\sin \theta+\cos \theta=\frac{6}{5}$, we have $(\sin \theta+\cos \theta)^{2}=1+2 \sin \theta \cos \theta=\frac{36}{25}$, which gives $\sin \theta \cos \theta=\frac{11}{50}$. Hence, $\tan \theta+\cot \theta=\frac{50}{11}$.