Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 38 (page 501)

Establish each identity.
$\frac{\cos 鈦� (伪) + \cos 鈦� (尾)}{\cos 鈦� (伪) 鈭� \cos 鈦� (尾)}$

Short Answer

Expert verified

$鈭� \cot 鈦� (\frac{伪 + 尾}{2}) \cot 鈦� (\frac{伪鈭� 尾}{2})$

Step by step solution

Step 1. Given information

We have been given $\frac{\cos 鈦� (伪) + \cos 鈦� (尾)}{\cos 鈦� (伪) 鈭� \cos 鈦� (尾)}$ .

We have to establish identity.

Step 2. Solve for the numerator part first

Numerator of the given expression has the form $\cos 伪 + \cos 尾$

Therefore, we get

$\cos 伪 + \cos 尾 = 2 \cos 鈦� (\frac{伪 + 尾}{2}) \cos 鈦� (\frac{伪鈭� 尾}{2})$

Step 3. Solve for the denominator part

Denominator of the given expression has the form $\cos 伪 - \cos 尾$

Therefore, we get

$\cos 伪 - \cos 尾 = 鈭� 2 \sin 鈦� (\frac{伪 + 尾}{2}) \sin 鈦� (\frac{伪鈭� 尾}{2})$

Step 4. Plug the above result

Plug the above results in the expression:

$\begin{aligned} \frac{\cos 鈦� (伪) + \cos 鈦� (尾)}{\cos 鈦� (伪) 鈭� \cos 鈦� (尾)} = \frac{2 \cos 鈦� (\frac{伪 + 尾}{2}) \cos 鈦� (\frac{伪鈭� 尾}{2})}{鈭� 2 \sin 鈦� (\frac{伪 + 尾}{2}) \sin 鈦� (\frac{伪鈭� 尾}{2})} \\ = (鈭� \frac{\cos 鈦� (\frac{伪 + 尾}{2})}{\sin 鈦� (\frac{伪 + 尾}{2})}) (\frac{\cos 鈦� (\frac{伪鈭� 尾}{2})}{\sin 鈦� (\frac{伪鈭� 尾}{2})}) \\ = 鈭� \cot 鈦� (\frac{伪 + 尾}{2}) \cot 鈦� (\frac{伪鈭� 尾}{2}) \end{aligned}$

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91影视

Establish each identity.
$\frac{\cos 鈦� (伪) + \cos 鈦� (尾)}{\cos 鈦� (伪) 鈭� \cos 鈦� (尾)}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for the numerator part first

Step 3. Solve for the denominator part

Step 4. Plug the above result

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91影视

Establish each identity.cos鈦�(伪)+cos鈦�(尾)cos鈦�(伪)鈭�cos鈦�(尾)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for the numerator part first

Step 3. Solve for the denominator part

Step 4. Plug the above result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Calculus

Mechanics Maths

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Establish each identity.
$\frac{\cos 鈦� (伪) + \cos 鈦� (尾)}{\cos 鈦� (伪) 鈭� \cos 鈦� (尾)}$