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Q40.

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Precalculus Mathematics for Calculus

Found in: Page 543

Book edition 7th Edition

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

Pages 948 pages

ISBN 9781337067508

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Short Answer

Question: Proving Identities
Verify the identity ${(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x$

The expression ${(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x$ is an identity.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

An expression ${(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x$

Step 2. Concept used.

Do two time simplification. First time, simplify the LHS part of the expression and second time simplify the RHS part of the expression. If both come out be equal then the expression is an identity.

Step 3. Calculation.

Now, simplify LHS of ${(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x$ :

${(\sin x + \cos x)}^{2} {(\sin x + \cos x)}^{2} = \sin^{2} x + \cos^{2} x + 2 \sin x \cos x ∵ \sin^{2} x + \cos^{2} x = 1 {(\sin x + \cos x)}^{2} = 1 + 2 \sin x \cos x$

RHS of the equation is $1 + 2 \sin x \cos x$

Both RHS and LHS are equal. Hence it is an identity.

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