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Expert-verified Found in: Page 542 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Simplifying Trigonometric Expressions-Write the trigonometric expression $\mathbit{t}\mathbit{a}\mathbit{n}\mathbit{\theta }\mathbit{c}\mathbit{s}\mathbit{c}\mathbit{\theta }$ in terms of sine and cosine, and then simplify.

On simplifying expression we get $\frac{1}{\mathrm{cos}\theta }$

See the step by step solution

## Step 1. Given information

A trigonometric expression as $\mathrm{tan}\theta \mathrm{csc}\theta$

## Step 2. Concept used

Write the expression in sine and cosine terms first. Then, to reduce it further, apply trigonometric identities.

## Step 3. Calculation

Now, write $\mathrm{tan}\theta \mathrm{sec}\theta$ in form of $sineand\mathrm{cos}ine$:

$\begin{array}{l}\mathrm{tan}\theta =\frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }\\ \mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta }\\ \therefore \mathrm{tan}\theta \mathrm{csc}\theta =\frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }×\frac{1}{\mathrm{sin}\theta }\\ =\frac{1}{\mathrm{cos}\theta }\end{array}$ ### Want to see more solutions like these? 