Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises - Page 908: 39

1

By identity: $csc\theta=\frac{1}{sin\theta}$ and $cot\theta=\frac{cos\theta}{sin\theta}$ Therefore, $$=\frac{cos\theta\times\frac{1}{sin\theta}}{\frac{cos\theta}{sin\theta}}$$ Simplifying division by inverse multiplication of denominator $$=\frac{cos\theta}{sin\theta}\times{\frac{sin\theta}{cos\theta}}$$ Cancel out $sin\theta$ and $cos\theta$ $$=1$$