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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 12 (page 500)

Express the product $\sin 4 胃 \cos 6 胃$ as a sum containing only sines or only cosines.

Short Answer

Expert verified

$\sin 4 胃 \cos 6 胃 = \frac{\sin (10 胃) - \sin (2 胃)}{2}$

Step by step solution

Step 1. Given expression

$\sin 4 胃 \cos 6 胃$

Step 2. Rewriting the expression

$2 \sin A \cos B = \sin (A + B) + \sin (A - B) s o, \sin 4 胃 \cos 6 胃 = \frac{\sin (10 胃) + \sin (- 2 胃)}{2} = \frac{\sin (10 胃) - \sin (2 胃)}{2} (\sin (- 胃) = - \sin 胃$

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Most popular questions from this chapter

Establish each identity.

$\frac{1 - 2 \cos^{2} 胃}{\sin 胃 \cos 胃} = \tan 胃 - c o t 胃$

Show that the difference quotient for $f (x) = \cos x$ is given by

role="math" localid="1646431168099" $\frac{f (x + h) - f (x)}{h} = \frac{\cos (x + h) - \cos (x)}{h} = - \sin x 路 \frac{\sin h}{h} - \cos x 路 \frac{1 - \cos h}{h}$

Establish each identity.

$\frac{\cos 胃 + \sin 胃 - \sin^{3} 胃}{\sin 胃} = c o t 胃 + \cos^{2} 胃$

solve each equation on the interval

$0 鈮� 胃 < 2 蟺$

$\sin 胃 + \cos 胃 = \sqrt{2}$

Repeat Problem $107$ for $g (x) = \cos^{2} x$ .

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91影视

Express the product sin4胃cos6胃as a sum containing only sines or only cosines.

Short Answer

Step by step solution

Step 1. Given expression

Step 2. Rewriting the expression

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Express the product $\sin 4 胃 \cos 6 胃$ as a sum containing only sines or only cosines.