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Expert-verified Found in: Page 475 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Establish each identity.$sec\theta -\mathrm{cos}\theta =\mathrm{sin}\theta \mathrm{tan}\theta$

The left side of the given equation has been simplified to give the right side.

See the step by step solution

## Step 1. Given Information

The given equation is $sec\theta -\mathrm{cos}\theta =\mathrm{sin}\theta \mathrm{tan}\theta$

## Step 2. Calculation

Consider the left side of the given equation and simplify.

$sec\theta -\mathrm{cos}\theta =\frac{1}{\mathrm{cos}\theta }-\mathrm{cos}\theta \phantom{\rule{0ex}{0ex}}=\frac{1-{\mathrm{cos}}^{2}\theta }{\mathrm{cos}\theta }\phantom{\rule{0ex}{0ex}}=\frac{{\mathrm{sin}}^{2}\theta }{\mathrm{cos}\theta }\phantom{\rule{0ex}{0ex}}=\mathrm{sin}\theta \frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }\phantom{\rule{0ex}{0ex}}=\mathrm{sin}\theta \mathrm{tan}\theta$

Thus, the given identity is established. ### Want to see more solutions like these? 