#### Answer

$$\cos^2\frac{\pi}{6}-\sin^2\frac{\pi}{6}=\frac{1}{2}$$
4 would be matched with A.

#### Work Step by Step

$$X=\cos^2\frac{\pi}{6}-\sin^2\frac{\pi}{6}$$
From the double-angle identities:
$$\cos^2 A-\sin^2 A=\cos2A$$
Thus $X$ can be seen here as $\cos^2 A-\sin^2 A$ with $A=\frac{\pi}{6}$.
Therefore,
$$X=\cos\Big(2\times\frac{\pi}{6}\Big)$$
$$X=\cos\frac{\pi}{3}$$
$$X=\frac{1}{2}$$
So, $$\cos^2\frac{\pi}{6}-\sin^2\frac{\pi}{6}=\frac{1}{2}$$
4 would be matched with A.