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Simplify the expression:
[tex]\[ x \cos x - \sin x \][/tex]

Sagot :

GinnyAnswer
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.

So, the expression you're looking for is:

[tex]\[ x \cos x - \sin x \][/tex]
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