Chapter 7: Q. 15 (page 500)

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

Short Answer

Expert verified

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

Step by step solution

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

Short Answer

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 cosinessin3ϑ2cosϑ2

Short Answer

Step by step solution

Step 1. Given expression

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

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