Sure! Let's break down the expression [tex]\( x \cos x - \sin x \)[/tex] step by step.
### Step-by-Step Solution
1. Expression Setup: We begin with the expression [tex]\[
x \cos x - \sin x
\][/tex] where [tex]\( x \)[/tex] is a variable.
2. Understanding Each Term: - The first term [tex]\( x \cos x \)[/tex] represents the product of [tex]\( x \)[/tex] and [tex]\( \cos x \)[/tex]. - The second term [tex]\( \sin x \)[/tex] is a trigonometric function of [tex]\( x \)[/tex].
3. Combining the Terms: In the given expression, we are subtracting the second term from the first term.
[tex]\[
x \cos x - \sin x
\][/tex] This combination results in a new function which involves both an oscillatory (cosine and sine) part and a linear part ([tex]\( x \)[/tex]).
4. Result: After combining the linear and trigonometric components, the final expression remains as: [tex]\[
x \cos x - \sin x
\][/tex]
### Conclusion
The given mathematical expression [tex]\( x \cos x - \sin x \)[/tex] does not simplify further using elementary algebraic methods. This is the final form of the expression after combining the individual terms.
