The expression in the image appears to be:

$\cos(x) \cdot (-\sin(x) + \cos(x)).$

Let me simplify this expression for you:

Step 1: Expand the terms

$\cos(x) \cdot (-\sin(x) + \cos(x)) = \cos(x) \cdot (-\sin(x)) + \cos(x) \cdot \cos(x).$

Step 2: Simplify each term

$\cos(x) \cdot (-\sin(x)) = -\cos(x) \sin(x),$ $\cos(x) \cdot \cos(x) = \cos^2(x).$

Step 3: Combine terms

$-\cos(x) \sin(x) + \cos^2(x).$

So, the simplified expression is: $\cos^2(x) - \cos(x) \sin(x).$

Let me know if you have further questions or need more clarification!

Related Questions:

1. How would you use trigonometric identities to simplify this further, if possible?
2. Can you plot this expression for different values of $x$?
3. What are the critical points of this expression?
4. How would you find the derivative of this expression?
5. How does this expression behave as $x$ approaches infinity?

Tip:

Always check for common trigonometric identities (like $\sin^2(x) + \cos^2(x) = 1$) when simplifying expressions!