# Chapter 5 - Section 5.1 - Verifying Trigonometric Identities - Exercise Set - Page 659: 24

See the explanation below.

#### Work Step by Step

$\frac{1-\sin \theta }{\cos \theta }=\sec \theta -\tan \theta$ Recall Trigonometric Identities, \begin{align} & \tan \theta =\frac{\sin \theta }{\cos \theta } \\ & \sec \theta =\frac{1}{\cos \theta } \\ \end{align} Use the above identities and solve the left side of the given expression, \begin{align} & \frac{1-\sin \theta }{\cos \theta }=\frac{1}{\cos \theta }-\frac{\sin \theta }{\cos \theta } \\ & =\sec \theta -\tan \theta \end{align} Therefore, $\frac{1-\sin \theta }{\cos \theta }=\sec \theta -\tan \theta$

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