Evaluate 2cos(pi/6)^2

$2 \cos^{2} (\frac{π}{6})$

Step 1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$2 {(\frac{\sqrt{3}}{2})}^{2}$

Step 2

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

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

Step 3

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$2 \frac{{(3^{\frac{1}{2}})}^{2}}{2^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \frac{3^{\frac{1}{2} \cdot 2}}{2^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$2 \frac{3^{\frac{2}{2}}}{2^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{3^{\frac{2}{2}}}{2^{2}}$

Rewrite the expression.

$2 \frac{3^{1}}{2^{2}}$

Evaluate the exponent.

$2 \frac{3}{2^{2}}$

Step 4

Raise $2$ to the power of $2$ .

$2 (\frac{3}{4})$

Step 5

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 \frac{3}{2 (2)}$

Cancel the common factor.

$2 \frac{3}{2 \cdot 2}$

Rewrite the expression.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$