S. 2 Simplify the following expeasion to a single irigatominetric tein. $$ \frac{\sin \left(360^{2}-x\right) \cdot \tan (-x)}{\cos \left(1800^{3}+x\right)\left(\sin ^{2} A+\cos ^{2} A\right)} $$ S.2. Simplify fully; $$ \frac{\sin 192^{\circ} \cdot \tan 300^{\circ} \cos \left(2070^{2}+x\right)}{\sin \left(-x-100^{\circ}\right) \cdot \cos 107^{\circ}} $$

Question

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Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(\sin\left(360^{2}-x\right)\tan\left(-x\right)\right)}{\left(\cos\left(1800^{3}+x\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)\right)}$$
- step1: Remove the parentheses:
  $$\frac{\sin\left(360^{2}-x\right)\tan\left(-x\right)}{\cos\left(1800^{3}+x\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step2: Transform the expression:
  $$\frac{\sin\left(360^{2}-x\right)\left(-\tan\left(x\right)\right)}{\cos\left(1800^{3}+x\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step3: Rewrite the expression:
  $$\frac{\sin\left(360^{2}-x\right)\left(-\tan\left(x\right)\right)}{\cos\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step4: Rewrite the expression:
  $$\frac{-\sin\left(360^{2}-x\right)\tan\left(x\right)}{\cos\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step5: Rewrite the fraction:
  $$-\frac{\sin\left(360^{2}-x\right)\tan\left(x\right)}{\cos\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step6: Rewrite the expression:
  $$-\cos^{-1}\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)^{-1}\sin\left(360^{2}-x\right)\tan\left(x\right)$$
- step7: Calculate:
  $$-\cos^{-1}\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)^{-1}\sin\left(360^{2}-x\right)\times \frac{\sin\left(x\right)}{\cos\left(x\right)}$$
- step8: Calculate:
  $$-\frac{\sin\left(360^{2}-x\right)\sin\left(x\right)}{\cos\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)\cos\left(x\right)}$$
- step9: Rewrite the expression:
  $$-\frac{\sin\left(x\right)\sin\left(360^{2}-x\right)}{\cos\left(x\right)\cos\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)}$$
- step10: Rewrite the expression:
  $$-\cos^{-1}\left(x\right)\cos^{-1}\left(x+1800^{3}\right)\left(\sin\left(A^{2}\right)+\cos\left(A^{2}\right)\right)^{-1}\sin\left(x\right)\sin\left(360^{2}-x\right)$$
- step11: Rewrite the expression:
  $$-\left(\sin\left(A^{2}\right)\cos\left(x+1800^{3}\right)\cos\left(x\right)+\cos\left(A^{2}\right)\cos\left(x+1800^{3}\right)\cos\left(x\right)\right)^{-1}\sin\left(x\right)\sin\left(360^{2}-x\right)$$
- step12: Rewrite the expression:
  $$-\left(\sin\left(A^{2}\right)\cos\left(x\right)\cos\left(x+1800^{3}\right)+\cos\left(A^{2}\right)\cos\left(x\right)\cos\left(x+1800^{3}\right)\right)^{-1}\sin\left(x\right)\sin\left(360^{2}-x\right)$$
- step13: Calculate:
  $$-\frac{\sin\left(x\right)\sin\left(360^{2}-x\right)}{\sin\left(A^{2}\right)\cos\left(x\right)\cos\left(x+1800^{3}\right)+\cos\left(A^{2}\right)\cos\left(x\right)\cos\left(x+1800^{3}\right)}$$
Let's simplify the first expression step by step:

### Expression 1:
$$
\frac{\sin \left(360^{2}-x\right) \cdot \tan (-x)}{\cos \left(1800^{3}+x\right)\left(\sin ^{2} A+\cos ^{2} A\right)}
$$

1. **Simplify $$\tan(-x)$$**:
   $$
   \tan(-x) = -\tan(x)
   $$

2. **Use the Pythagorean identity**:
   $$
   \sin^2 A + \cos^2 A = 1
   $$
   Thus, the denominator simplifies to:
   $$
   \cos(1800^3 + x)
   $$

3. **Rewrite the expression**:
   $$
   \frac{\sin(360^2 - x) \cdot (-\tan(x))}{\cos(1800^3 + x)}
   $$

4. **Substituting $$\tan(x)$$**:
   $$
   \tan(x) = \frac{\sin(x)}{\cos(x)}
   $$
   Therefore, the expression becomes:
   $$
   -\frac{\sin(360^2 - x) \cdot \sin(x)}{\cos(1800^3 + x) \cdot \cos(x)}
   $$

Now, let's simplify the second expression:

### Expression 2:
$$
\frac{\sin 192^{\circ} \cdot \tan 300^{\circ} \cos \left(2070^{2}+x\right)}{\sin \left(-x-100^{\circ}\right) \cdot \cos 107^{\circ}}
$$

1. **Simplify $$\tan(300^{\circ})$$**:
   $$
   \tan(300^{\circ}) = \tan(360^{\circ} - 60^{\circ}) = -\tan(60^{\circ}) = -\sqrt{3}
   $$

2. **Rewrite the expression**:
   $$
   \frac{\sin(192^{\circ}) \cdot (-\sqrt{3}) \cdot \cos(2070^{2} + x)}{\sin(-x - 100^{\circ}) \cdot \cos(107^{\circ})}
   $$

3. **Use the identity for $$\sin(-\theta)$$**:
   $$
   \sin(-\theta) = -\sin(\theta)
   $$
   Thus, $$\sin(-x - 100^{\circ}) = -\sin(x + 100^{\circ})$$.

4. **Final expression**:
   $$
   \frac{-\sin(192^{\circ}) \cdot (-\sqrt{3}) \cdot \cos(2070^{2} + x)}{-\sin(x + 100^{\circ}) \cdot \cos(107^{\circ})}
   $$
   This simplifies to:
   $$
   \frac{\sqrt{3} \cdot \sin(192^{\circ}) \cdot \cos(2070^{2} + x)}{\sin(x + 100^{\circ}) \cdot \cos(107^{\circ})}
   $$

### Summary of Results:
1. The first expression simplifies to:
   $$
   -\frac{\sin(360^2 - x) \cdot \sin(x)}{\cos(1800^3 + x) \cdot \cos(x)}
   $$

2. The second expression simplifies to:
   $$
   \frac{\sqrt{3} \cdot \sin(192^{\circ}) \cdot \cos(2070^{2} + x)}{\sin(x + 100^{\circ}) \cdot \cos(107^{\circ})}
   $$
The first expression simplifies to: $$ -\frac{\sin(360^2 - x) \cdot \sin(x)}{\cos(1800^3 + x) \cdot \cos(x)} $$ The second expression simplifies to: $$ \frac{\sqrt{3} \cdot \sin(192^{\circ}) \cdot \cos(2070^{2} + x)}{\sin(x + 100^{\circ}) \cdot \cos(107^{\circ})} $$

S. 2 Simplify the following expeasion to a single irigatominetric tein.

S.2. Simplify fully;

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S. 2 Simplify the following expeasion to a single irigatominetric tein. S.2. Simplify fully;