1. We need to evaluate $\cos 210^\circ - \cos 10^\circ \cos 50^\circ + \cos 250^\circ.$

2. First simplify the individual cosine terms using angle identities:

• $\cos 210^\circ = \cos(180^\circ+30^\circ) = -\cos 30^\circ = -\frac{\sqrt{3}}{2}.$
• $\cos 250^\circ = \cos(180^\circ+70^\circ) = -\cos 70^\circ = -\sin 20^\circ.$

So the expression becomes -rac{\sqrt{3}}{2} - \cos 10^\circ\cos 50^\circ - \sin 20^\circ.

3. Now simplify the product $\cos 10^\circ\cos 50^\circ$ using $\cos A\cos B = \frac{1}{2}\big[\cos(A-B)+\cos(A+B)\big].$ Thus, $\cos 10^\circ\cos 50^\circ = \frac{1}{2}\big[\cos 40^\circ + \cos 60^\circ\big].$ Since $\cos 60^\circ=\frac12$, $\cos 10^\circ\cos 50^\circ = \frac{1}{2}\cos 40^\circ + \frac{1}{4}.$

Hence the expression is -rac{\sqrt{3}}{2} - \left(\frac{1}{2}\cos 40^\circ + \frac{1}{4}\right) - \sin 20^\circ. That is, -rac{\sqrt{3}}{2} - \frac{1}{2}\cos 40^\circ - \frac{1}{4} - \sin 20^\circ.

4. This does not look like any option, so let us check the sign carefully by combining the first and third terms directly:

$\cos 210^\circ + \cos 250^\circ.$ Using $\cos C + \cos D = 2\cos\frac{C+D}{2}\cos\frac{C-D}{2},$ we get $\cos 210^\circ + \cos 250^\circ = 2\cos 230^\circ \cos 20^\circ.$ Now, $\cos 230^\circ = \cos(180^\circ+50^\circ) = -\cos 50^\circ,$ so $\cos 210^\circ + \cos 250^\circ = -2\cos 50^\circ\cos 20^\circ.$

Therefore the whole expression is $-2\cos 50^\circ\cos 20^\circ - \cos 10^\circ\cos 50^\circ.$ Factor out $-\cos 50^\circ$: $=-\cos 50^\circ\big(2\cos 20^\circ+\cos 10^\circ\big).$ This again is clearly negative, whereas all options are positive. So there is likely a typo in the question statement.

5. Let us test the most likely intended expression, which is often $\cos 210^\circ - \cos 10^\circ\cos 50^\circ + \cos 230^\circ,$ or some nearby angle; but with the given expression $250^\circ$, the value is not equal to any listed option.

6. Numerical check of the given expression: $\cos 210^\circ = -0.8660,$ $\cos 10^\circ\cos 50^\circ \approx 0.9848\times 0.6428 \approx 0.6330,$ $\cos 250^\circ \approx -0.3420.$ So, $-0.8660 - 0.6330 - 0.3420 \approx -1.8410.$ This is not equal to $\frac34$.

7. Therefore, for the expression as written, none of the options is correct. The stored answer $B$ does not match the actual evaluation of the given expression.