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Q 95.

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Precalculus Mathematics for Calculus

Found in: Page 544

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Determining Identities Graphically
Graph $f$ and $g$ in the same viewing rectangle. Do the graphs suggest that the equation $f (x) = g (x)$ is an identity? Prove your answer
$f (x) = c o s^{2} x - s i n^{2} x, g (x) = 1 - 2 s i n^{2} x$

The expression $f (x) = g (x)$ is an identity.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Two functions as-

$\begin{array}{l} f (x) = \cos^{2} x - \sin^{2} x \\ g (x) = 1 - 2 \sin^{2} x \end{array}$

Step 2. Concept used

Create distinct graphs for both functions on the same graph. Both functions are equivalent if both graphs coincide with one other. As a result, combining them into a single equation yields an identity.

Step 3. Calculation

Now, draw graphs of both functions:

Since both graphs coincide each other. Therefore $f (x) = g (x)$ is an identity

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