Find the Exact Value 2(cos(15 degrees )^2-sin(15 degrees )^2)

$2 (\cos^{2} (15 °) - \sin^{2} (15 °))$

Step 1

Apply the cosine double-angle identity.

$2 \cos (2 \cdot 15 °)$

Step 2

Multiply $2$ by $15 °$ .

$2 \cos (30)$

Step 3

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$2 \frac{\sqrt{3}}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{\sqrt{3}}{2}$

Rewrite the expression.

$\sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$