Chapter 7: Q. 16 (page 500)

express each product as a sum containing only sines or only cosines
$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2}$

Short Answer

Expert verified

$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2} = \frac{1}{2} [\sin (3 ϑ) - \sin (2 ϑ)]$

Step by step solution

Step 1. Given expression

$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2}$

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 :

$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2} = \frac{1}{2} [\sin (\frac{5 ϑ}{2} + \frac{ϑ}{2}) - \sin (\frac{5 ϑ}{2} - \frac{ϑ}{2})] \sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2} = \frac{1}{2} [\sin (3 ϑ) - \sin (2 ϑ)]$

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express each product as a sum containing only sines or only cosines
$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2}$

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 cosinessinϑ2cos5ϑ2

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

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

express each product as a sum containing only sines or only cosines
$\sin \frac{ϑ}{2} \cos \frac{5 ϑ}{2}$