Q. 111 Explain why formula cannot be us... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 111 (page 487)

Explain why formula cannot be used to show that
$\tan (\frac{蟺}{2} - 胃) = c o t 胃$
Establish this identity by using formulas $(3 a)$ and $(3 b)$ .

Short Answer

Expert verified

The equation $\tan (\frac{蟺}{2} - 胃) = c o t 胃$ cannot be derived using the formula $\tan (伪 + 尾) = \frac{\tan (伪) + \tan (尾)}{1 - \tan (伪) \tan (尾)}$ becouse this derivation will consist of $\tan \frac{蟺}{2}$ , which is undefined and makes the further steps undefined

the correct derivation is

$\tan (胃 + \frac{蟺}{2}) = \frac{\sin (胃 + \frac{蟺}{2})}{\cos (胃 + \frac{蟺}{2})} = \frac{\sin 胃 \cos \frac{蟺}{2} + \cos 胃 \sin \frac{蟺}{2}}{\cos 胃 \cos \frac{蟺}{2} - \sin 胃 \sin \frac{蟺}{2}} = \frac{0 + \cos 胃}{0 - \sin 胃} = c o t 胃$

Step by step solution

Step 1. Given data

The given formula is

$\tan (伪 + 尾) = \frac{\tan (伪) + \tan (尾)}{1 - \tan (伪) \tan (尾)}$

The equation we need to prove is

$\tan (\frac{蟺}{2} - 胃) = c o t 胃$

Step 2. Clarification

Derivation using formula $\tan (伪 + 尾) = \frac{\tan (伪) + \tan (尾)}{1 - \tan (伪) \tan (尾)}$

$\tan (胃 + \frac{蟺}{2}) = \frac{\tan (胃) + \tan (\frac{蟺}{2})}{1 - \tan (胃) \tan (\frac{蟺}{2})} = \frac{\frac{\tan (胃)}{\tan (\frac{蟺}{2})} + 1}{\frac{1}{\tan (\frac{蟺}{2})} - \tan (胃)}$

Not the expression consists of $\tan \frac{蟺}{2}$

which is undefined so the further derivation is not possible

Step 3. correct derivation

Derivation of the equation

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91影视

Explain why formula cannot be used to show that
$\tan (\frac{蟺}{2} - 胃) = c o t 胃$
Establish this identity by using formulas $(3 a)$ and $(3 b)$ .

Short Answer

Step by step solution

Step 1. Given data

Step 2. Clarification

Step 3. correct derivation

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91影视

Explain why formula cannot be used to show thattan蟺2-胃=cot胃Establish this identity by using formulas (3a)and(3b).

Short Answer

Step by step solution

Step 1. Given data

Step 2. Clarification

Step 3. correct derivation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Probability and Statistics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Explain why formula cannot be used to show that
$\tan (\frac{蟺}{2} - 胃) = c o t 胃$
Establish this identity by using formulas $(3 a)$ and $(3 b)$ .