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

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

1. Evaluate \( \sin \frac{13\pi}{2} \): \[ \frac{13\pi}{2} = 6\pi + \frac{\pi}{2} \] Using the periodicity of sine (\(\sin x = \sin(x + 2\pi k)\)), we have: \[ \sin \frac{13\pi}{2} = \sin \frac{\pi}{2} = 1 \]

2. Evaluate \( -\cos \frac{3\pi}{2} \): \[ \cos \frac{3\pi}{2} = 0 \] Hence: \[ -\cos \frac{3\pi}{2} = 0 \]

3. Evaluate \( \cos 12\pi \): \[ \cos 12\pi = \cos(6 \times 2\pi) = 1 \]

4. Evaluate \( \cot(-\frac{3\pi}{2}) \): \[ \cot(-\frac{3\pi}{2}) = \frac{1}{\tan(-\frac{3\pi}{2})} \] The angle \(-\frac{3\pi}{2}\) is equivalent to \(\frac{\pi}{2}\): \[ \tan(-\frac{3\pi}{2}) = \tan(\frac{\pi}{2} + 2\pi k) \text{ is undefined} \] Thus, \( \cot(-\frac{3\pi}{2}) = 0 \) because the cotangent of undefined values isn't defined.

Now substituting everything into the expression: \[ \sin \frac{13\pi}{2} - \cos \frac{3\pi}{2} + \cos 12\pi - \tan(*) + \cot(-\frac{3\pi}{2}) = 1 - 0 + 1 - \tan(*) + 0 \] This simplifies to:

\[ 2 - \tan(*) \]

Now, without the value for \(\tan(*)\), we can't fully complete the calculation, but we can conclude: \[ \sin \frac{13\pi}{2} - \cos \frac{3\pi}{2} + \cos 12\pi - \tan(*) + \cot(-\frac{3\pi}{2}) = 2 - \tan(*) \]

Please provide the specific value for the angle where you need the tangent computation to obtain the final result!