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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. $\frac{\mathrm{cos}\theta +\mathrm{sin}\theta -{\mathrm{sin}}^{3}\theta }{\mathrm{sin}\theta }=cot\theta +{\mathrm{cos}}^{2}\theta$

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

See the step by step solution

## Step 1. Given Information

The given equation is $\frac{\mathrm{cos}\theta +\mathrm{sin}\theta -{\mathrm{sin}}^{3}\theta }{\mathrm{sin}\theta }=cot\theta +{\mathrm{cos}}^{2}\theta$

## Step 2. Calculation

Consider the left side of the given equation and simplify to bring the right side in order to establish the equation.

$\frac{\mathrm{cos}\theta +\mathrm{sin}\theta -{\mathrm{sin}}^{3}\theta }{\mathrm{sin}\theta }=\frac{\mathrm{cos}\theta }{\mathrm{sin}\theta }+\frac{\mathrm{sin}\theta }{\mathrm{sin}\theta }-\frac{{\mathrm{sin}}^{3}\theta }{\mathrm{sin}\theta }\phantom{\rule{0ex}{0ex}}=cot\theta +1-{\mathrm{sin}}^{2}\theta \phantom{\rule{0ex}{0ex}}=cot\theta +{\mathrm{cos}}^{2}\theta$

Hence, Proved ### Want to see more solutions like these? 