## Trigonometry (10th Edition)

$$\frac{1}{\sin\theta\cos\theta}$$ $$or$$ $$\csc\theta\sec\theta$$
$$\cot\theta+\frac{1}{\cot\theta}$$ Multiply $\cot\theta$ by $\frac{\cot\theta}{\cot\theta}$ to get common denominators: $$\frac{\cot^{2}\theta}{\cot\theta}+\frac{1}{\cot\theta}$$ $$=\frac{\cot^{2}\theta+1}{\cot\theta}$$ $\cot^{2}\theta+1=\csc^{2}\theta$ because of the Pythagorean Identities $$=\frac{\csc^{2}\theta}{\cot\theta}$$ Rewrite using Reciprocal Identities: $$=\frac{1}{\sin^{2}\theta}\div\frac{\cos\theta}{\sin\theta}$$ $$=\frac{1}{\sin^{2}\theta}\times\frac{\sin\theta}{\cos\theta}$$ $$=\frac{1}{\sin\theta\cos\theta}=\csc\theta\sec\theta$$