Find the Exact Value cos(pi/6)^2-sin(pi/6)^2

$\cos^{2} (\frac{π}{6}) - \sin^{2} (\frac{π}{6})$

Step 1

Apply the cosine double-angle identity.

$\cos (2 \frac{π}{6})$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\cos (2 \frac{π}{2 (3)})$

Cancel the common factor.

$\cos (2 \frac{π}{2 \cdot 3})$

Rewrite the expression.

$\cos (\frac{π}{3})$

Step 3

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$