Short Answer

express each product as a sum containing only sines or only cosines
$\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2}$

$\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2} = \frac{1}{2} [\sin (2 ϑ) + \sin (ϑ)]$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given expression

$\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2}$

Step 2. expressing them in terms of single sine or cosine

Using identity :

$\sin x + \sin y = 2 \sin \frac{x + y}{2} \cos \frac{x - y}{2}$

We get :

role="math" localid="1646448141774" $\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2} = \frac{1}{2} [\sin (\frac{3 ϑ}{2} + \frac{ϑ}{2}) + \sin (\frac{3 ϑ}{2} - \frac{ϑ}{2}) \sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2} = \frac{1}{2} [\sin (2 ϑ) + \sin (ϑ)]$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

express each product as a sum containing only sines or only cosines
$\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2}$

Step by Step Solution

Step 1. Given expression

Step 2. expressing them in terms of single sine or cosine

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Precalculus Enhanced with Graphing Utilities

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Short Answer

express each product as a sum containing only sines or only cosines sin 3ϑ2cosϑ2

Step by Step Solution

Step 1. Given expression

Step 2. expressing them in terms of single sine or cosine

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express each product as a sum containing only sines or only cosines
$\sin \frac{3 ϑ}{2} \cos \frac{ϑ}{2}$