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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. 1 (page 495)

$\cos (2 胃) = \cos^{2} 胃 -$ $=$ $- 1 = 1 -$ .

Short Answer

Expert verified

$\cos (2 胃) = {(\cos 胃)}^{2} - \underset{铃�}{{(\sin 胃)}^{2}} = \underset{铃�}{{2 (\cos 胃)}^{2}} - 1 = 1 - \underset{铃�}{{2 (\sin 胃)}^{2}}$ .

Step by step solution

01

Step 1. Given Data

The given incomplete equation is

$\cos (2 胃) = \cos^{2} 胃 -____=_____- 1 = 1 -______$

02

Step 2. Explanation

Use Sum formula of the cosine function

$\cos (胃 + 胃) = (\cos 胃) (\cos 胃) - (\sin 胃) (\sin 胃) \cos (2 胃) = {(\cos 胃)}^{2} - {(\sin 胃)}^{2} \cos (2 胃) = 1 - {(\sin 胃)}^{2} - {(\sin 胃)}^{2} \cos (2 胃) = 1 - {2 (\sin 胃)}^{2}$

and

$\cos (2 胃) = {(\cos 胃)}^{2} - (1 - {(\cos 胃)}^{2}) \cos (2 胃) = 2 {(\cos 胃)}^{2} - 1$

so $\cos (2 胃) = {(\cos 胃)}^{2} - \underset{铃�}{{(\sin 胃)}^{2}} = \underset{铃�}{{2 (\cos 胃)}^{2}} - 1 = 1 - \underset{铃�}{{2 (\sin 胃)}^{2}}$

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Most popular questions from this chapter

Establish each identity.

${(2 a \sin 胃 \cos 胃)}^{2} + a^{2} {(\cos^{2} 胃 - \sin^{2} 胃)}^{2} = a^{2}$

In Problems 9鈥�36, find the exact value of each expression.

$\cos^{- 1} (\sin \frac{5 蟺}{4})$

Multiply and simplify: $\frac{(1 + \tan (胃)) (1 + \tan (胃)) - s e c (胃)}{\tan (胃)}$

Multiply: $\frac{\cos (胃)}{1 - \sin (胃)} \frac{1 + \sin (胃)}{1 + \sin (胃)}$

Establish each identity.

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

See all solutions

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