The value of `cos^2(pi/6+theta)-sin ^2\ (pi/6-theta)` is `adot1/2cos\ 2theta` b. `0` c. `-1/2cos2theta` d. `1/2`

Explanation

To find the value of \( \cos^2\left(\frac{\pi}{6} + \theta\right) - \sin^2\left(\frac{\pi}{6} - \theta\right) \), we can use trigonometric identities. Let's break this down step by step.

### Step 1: Use the Cosine and Sine Square Identity
We know that:
\[ \cos^2 A - \sin^2 B = \cos(A + B) \cos(A - B) \]
In our case, let \( A = \frac{\pi}{6} + \theta \) and \( B = \frac{\pi}{6} - \theta \).
...