Answer :
Sure! Let's go through the steps to arrive at the expression [tex]\( x \cos(x) - \sin(x) \)[/tex].
### Step-by-Step Solution:
1. Identify Variables and Constants:
- We have a single variable in the expression, which is [tex]\( x \)[/tex].
2. Understanding Trigonometric Functions:
- The components of the expression are trigonometric functions involving [tex]\( x \)[/tex]. Specifically, we have [tex]\( \cos(x) \)[/tex] and [tex]\( \sin(x) \)[/tex].
3. Expression Components:
- We are given two terms:
1. [tex]\( x \cos(x) \)[/tex]
2. [tex]\( - \sin(x) \)[/tex]
4. Combine Terms:
- Since these are the two terms of the expression, we combine them to write the full expression.
### Final Expression:
The final expression that results from combining the components [tex]\( x \cos(x) \)[/tex] and [tex]\( - \sin(x) \)[/tex] is:
[tex]\[ x \cos(x) - \sin(x) \][/tex]
That’s the combined and simplified form of the expression involving the variable [tex]\( x \)[/tex] with trigonometric functions [tex]\( \cos \)[/tex] and [tex]\( \sin \)[/tex].
### Step-by-Step Solution:
1. Identify Variables and Constants:
- We have a single variable in the expression, which is [tex]\( x \)[/tex].
2. Understanding Trigonometric Functions:
- The components of the expression are trigonometric functions involving [tex]\( x \)[/tex]. Specifically, we have [tex]\( \cos(x) \)[/tex] and [tex]\( \sin(x) \)[/tex].
3. Expression Components:
- We are given two terms:
1. [tex]\( x \cos(x) \)[/tex]
2. [tex]\( - \sin(x) \)[/tex]
4. Combine Terms:
- Since these are the two terms of the expression, we combine them to write the full expression.
### Final Expression:
The final expression that results from combining the components [tex]\( x \cos(x) \)[/tex] and [tex]\( - \sin(x) \)[/tex] is:
[tex]\[ x \cos(x) - \sin(x) \][/tex]
That’s the combined and simplified form of the expression involving the variable [tex]\( x \)[/tex] with trigonometric functions [tex]\( \cos \)[/tex] and [tex]\( \sin \)[/tex].
