Simplig the ff: friconometric expressin $$ \frac{\cos \left(360^{\circ}-x\right) \cdot \operatorname{Sin}\left(360^{\circ}-x\right) \cdot \operatorname{Cos}\left(90^{\circ}-x\right)}{\sin ^{2}\left(00^{\circ}-x\right) \cdot \operatorname{Sin}\left(180^{\circ}+x\right)} $$

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We start with the expression
$$
\frac{\cos\left(360^\circ-x\right)\cdot\sin\left(360^\circ-x\right)\cdot\cos\left(90^\circ-x\right)}{\sin^2\left(0^\circ-x\right)\cdot\sin\left(180^\circ+x\right)}.
$$

**Step 1. Simplify the angles using trigonometric identities:**

- Using the periodic property of cosine,
  $$
  \cos(360^\circ-x)=\cos x.
  $$
- For sine,
  $$
  \sin(360^\circ-x)=-\sin x,
  $$
  because
  $$
  \sin(360^\circ-x)=\sin 360^\circ\cos x-\cos 360^\circ\sin x=0\cdot\cos x-\sin x=-\sin x.
  $$
- For cosine of the complementary angle,
  $$
  \cos(90^\circ-x)=\sin x.
  $$
- Note that
  $$
  \sin(0^\circ-x)=\sin(-x)=-\sin x,
  $$
  so
  $$
  \sin^2(0^\circ-x)=\sin^2 x.
  $$
- And
  $$
  \sin(180^\circ+x)=-\sin x.
  $$

**Step 2. Substitute these into the expression:**

$$
\frac{\cos x\cdot(-\sin x)\cdot\sin x}{\sin^2 x\cdot(-\sin x)}.
$$

**Step 3. Simplify the numerator and denominator:**

Multiply the factors in the numerator:
$$
\cos x\cdot(-\sin x)\cdot\sin x=-\cos x\,\sin^2 x.
$$
Multiply the factors in the denominator:
$$
\sin^2 x\cdot(-\sin x)=-\sin^3 x.
$$

So the expression becomes:
$$
\frac{-\cos x \, \sin^2 x}{-\sin^3 x}.
$$

**Step 4. Cancel common factors:**

The minus signs cancel:
$$
\frac{\cos x\, \sin^2 x}{\sin^3 x}.
$$

Cancel $$\sin^2 x$$ in the numerator with part of $$\sin^3 x$$ in the denominator:
$$
\frac{\cos x}{\sin x}.
$$

This result is the definition of the cotangent:
$$
\frac{\cos x}{\sin x}=\cot x.
$$

Thus, the simplified expression is
$$
\cot x.
$$
The simplified expression is $$ \cot x $$.

Simplig the ff: friconometric expressin \( \frac{\cos \left(360^{\circ}-x\right) \cdot \operatorname{Sin}\left(360^{\circ}-x\right) \cdot \operatorname{Cos}\left(90^{\circ}-x\right)}{\sin ^{2}\left(00^{\circ}-x\right) \cdot \operatorname{Sin}\left(180^{\circ}+x\right)} \)

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