Sin 13пи/2-cos 3пи/2+cos12пи-tg*+ctg(-3пи/2)

To simplify the expression \( \sin\left(\frac{13\pi}{2}\right) - \cos\left(\frac{3\pi}{2}\right) + \cos(12\pi) - \tan(*) + \cot\left(-\frac{3\pi}{2}\right) \), we will evaluate each trigonometric function step by step.

1. Evaluate \( \sin\left(\frac{13\pi}{2}\right) \):

   • The angle \( \frac{13\pi}{2} \) is equivalent to \( \frac{13\pi}{2} - 6\pi = \frac{1\pi}{2} \) (since \( 6\pi \) is \( 3 \times 2\pi \)).
   • \( \sin\left(\frac{1\pi}{2}\right) = 1 \).

2. Evaluate \( -\cos\left(\frac{3\pi}{2}\right) \):

   • \( \cos\left(\frac{3\pi}{2}\right) = 0 \).
   • So, \( -\cos\left(\frac{3\pi}{2}\right) = 0 \).

3. Evaluate \( \cos(12\pi) \):

   • \( \cos(12\pi) = \cos(0) = 1 \).

4. Evaluate \( \tan(*) \):

   • \( \tan(*) \) cannot be evaluated without a specific value for the angle. We will keep this term as \( \tan(*) \).

5. Evaluate \( \cot\left(-\frac{3\pi}{2}\right) \):

   • \( \cot\left(-\frac{3\pi}{2}\right) = \frac{1}{\tan\left(-\frac{3\pi}{2}\right)} \).
   • Note that \( \tan\left(-\frac{3\pi}{2}\right) = \tan\left(\frac{\pi}{2}\right) \) which is undefined, thus \( \cot\left(-\frac{3\pi}{2}\right) \) is also undefined.

Putting everything together: \[ \sin\left(\frac{13\pi}{2}\right) - \cos\left(\frac{3\pi}{2}\right) + \cos(12\pi) - \tan(*) + \cot\left(-\frac{3\pi}{2}\right) = 1 + 0 + 1 - \tan(*) + \text{(undefined)} \]

Since one of the terms is undefined, the entire expression cannot be fully evaluated. Therefore, the expression is:

\[ \text{Undefined} \quad \text{(due to the } \cot\left(-\frac{3\pi}{2}\right) \text{ term)} \]