Find the Exact Value sin(pi/4)cos(pi/4)-tan(pi/3)

$\sin (\frac{π}{4}) \cos (\frac{π}{4}) - \tan (\frac{π}{3})$

Step 1

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cos (\frac{π}{4}) - \tan (\frac{π}{3})$

Step 2

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \tan (\frac{π}{3})$

Step 3

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2}$ .

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2} \sqrt{2}}{2 \cdot 2} - \tan (\frac{π}{3})$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} \sqrt{2}}{2 \cdot 2} - \tan (\frac{π}{3})$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}{2 \cdot 2} - \tan (\frac{π}{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt{2}}^{1 + 1}}{2 \cdot 2} - \tan (\frac{π}{3})$

Add $1$ and $1$ .

$\frac{{\sqrt{2}}^{2}}{2 \cdot 2} - \tan (\frac{π}{3})$

Multiply $2$ by $2$ .

$\frac{{\sqrt{2}}^{2}}{4} - \tan (\frac{π}{3})$

Step 4

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

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

$\frac{{(2^{\frac{1}{2}})}^{2}}{4} - \tan (\frac{π}{3})$

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

$\frac{2^{\frac{1}{2} \cdot 2}}{4} - \tan (\frac{π}{3})$

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

$\frac{2^{\frac{2}{2}}}{4} - \tan (\frac{π}{3})$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2^{\frac{2}{2}}}{4} - \tan (\frac{π}{3})$

Rewrite the expression.

$\frac{2^{1}}{4} - \tan (\frac{π}{3})$

Evaluate the exponent.

$\frac{2}{4} - \tan (\frac{π}{3})$

Step 5

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{4} - \tan (\frac{π}{3})$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2} - \tan (\frac{π}{3})$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2} - \tan (\frac{π}{3})$

Rewrite the expression.

$\frac{1}{2} - \tan (\frac{π}{3})$

Step 6

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

$\frac{1}{2} - \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2} - \sqrt{3}$

Decimal Form:

$- 1.23205080 \dots$

Find the Exact Value sin(pi/4)cos(pi/4)-tan(pi/3)

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