Chapter 7 - Section 7.1 - Trigonometric Identities - 7.1 Exercises - Page 543: 31

$\dfrac{\sin\theta}{\tan\theta}=\cos\theta$

$\dfrac{\sin\theta}{\tan\theta}=\cos\theta$ Substitute $\tan\theta$ with $\dfrac{\sin\theta}{\cos\theta}$ and simplify: $\dfrac{\sin\theta}{\Big(\dfrac{\sin\theta}{\cos\theta}\Big)}=\cos\theta$ $\dfrac{1}{\Big(\dfrac{1}{\cos\theta}\Big)}=\cos\theta$ $\cos\theta=\cos\theta$