Choose the correct answer from the drop-down menu. Find the exact value of \( \cos \frac{13 \pi}{12}+\cos \frac{7 \pi}{12} \). \[ \cos \frac{13 \pi}{12}+\cos \frac{7 \pi}{12}=\operatorname{select...} \] \[ \frac{\sqrt{2}}{2} \]

To find the exact value of \( \cos \frac{13 \pi}{12} + \cos \frac{7 \pi}{12} \), we can utilize the cosine addition formula and the properties of the angles in question. By converting these angles to more manageable forms, we can simplify the expression and discover the exact value using identities or numerical approximations. Another fun way to approach problems like this is to visualize the unit circle! Each cosine value corresponds to the x-coordinate of a point on the circle. So, as you add these two angles together, you're really adding their x-coordinates, which can sometimes lead to some unexpected but delightful results when you sum up those coordinates! Now, put your guessing cap on and take a look at those angles again for the best answer!