Using the sum and difference of cosines formula, find the exact value of cos (5). Enclose numerators and denominators in parentheses For example (a. b)/ (14 n)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need to know the steps on how to solve this problem. I am not sure where to begin.

**Problem Statement:**

Using the sum and difference of cosines formula, find the exact value of \( \cos \left( \frac{\pi}{12} \right) \).

**Instructions:**

Enclose numerators and denominators in parentheses. For example, express as \((a - b)/(1 + n)\).

**Interactive Input Box:**

- The box provided allows for input of mathematical expressions using buttons for various functions such as exponentiation \( a^b \), sine function \( \sin(a) \), and alpha notation \( \alpha \).

**Task:**

\[ \cos \left( \frac{\pi}{12} \right) = \]

**Note:**

Show your work and explain, in your own words, how you arrived at your answer.

---

**Hints for Solving:**

You can use the identity for the cosine of a sum or difference:

\[ 
\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b 
\]

Consider breaking down \( \frac{\pi}{12} \) using known angles like \( \frac{\pi}{6} \), \( \frac{\pi}{4} \), \( \frac{\pi}{3} \), etc.
Transcribed Image Text:**Problem Statement:** Using the sum and difference of cosines formula, find the exact value of \( \cos \left( \frac{\pi}{12} \right) \). **Instructions:** Enclose numerators and denominators in parentheses. For example, express as \((a - b)/(1 + n)\). **Interactive Input Box:** - The box provided allows for input of mathematical expressions using buttons for various functions such as exponentiation \( a^b \), sine function \( \sin(a) \), and alpha notation \( \alpha \). **Task:** \[ \cos \left( \frac{\pi}{12} \right) = \] **Note:** Show your work and explain, in your own words, how you arrived at your answer. --- **Hints for Solving:** You can use the identity for the cosine of a sum or difference: \[ \cos(a \pm b) = \cos a \cos b \mp \sin a \sin b \] Consider breaking down \( \frac{\pi}{12} \) using known angles like \( \frac{\pi}{6} \), \( \frac{\pi}{4} \), \( \frac{\pi}{3} \), etc.
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To find cosπ12

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