Evaluate sec(pi/4)tan(pi/4)

$\sec (\frac{π}{4}) \tan (\frac{π}{4})$

Step 1

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

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

Step 2

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

$\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \tan (\frac{π}{4})$

Step 3

Combine and simplify the denominator.

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

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

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

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

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

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

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

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1 + 1}} \tan (\frac{π}{4})$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $\sqrt{2}$ by $1$ .

$\sqrt{2} \tan (\frac{π}{4})$

Step 5

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\sqrt{2} \cdot 1$

Step 6

Multiply $\sqrt{2}$ by $1$ .

$\sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Evaluate sec(pi/4)tan(pi/4)

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