1) cos107∙cos17+sin107∙sin17; 2) cos 36∙cos 24+ sin 36∙sin24; 3) sin 63∙ cos 27+cos63∙sin 27; 4) sin51∙ cos 21+cos 51∙sin 21

The expressions you've provided can be simplified using the cosine and sine addition formulas. Here are the formulas:

• \(\cos A \cos B + \sin A \sin B = \cos(A - B)\)
• \(\sin A \cos B + \cos A \sin B = \sin(A + B)\)

Now we can simplify each expression:

1. For \( \cos 107 \cdot \cos 17 + \sin 107 \cdot \sin 17 \): \[ \cos 107 \cdot \cos 17 + \sin 107 \cdot \sin 17 = \cos(107 - 17) = \cos 90 = 0 \]

2. For \( \cos 36 \cdot \cos 24 + \sin 36 \cdot \sin 24 \): \[ \cos 36 \cdot \cos 24 + \sin 36 \cdot \sin 24 = \cos(36 - 24) = \cos 12 \]

3. For \( \sin 63 \cdot \cos 27 + \cos 63 \cdot \sin 27 \): \[ \sin 63 \cdot \cos 27 + \cos 63 \cdot \sin 27 = \sin(63 + 27) = \sin 90 = 1 \]

4. For \( \sin 51 \cdot \cos 21 + \cos 51 \cdot \sin 21 \): \[ \sin 51 \cdot \cos 21 + \cos 51 \cdot \sin 21 = \sin(51 + 21) = \sin 72 \]

Thus, the simplified results for the expressions are:

1. \(0\)
2. \(\cos 12\)
3. \(1\)
4. \(\sin 72\)