Trigonometry Examples

$\frac{1 - \tan (\frac{π}{4})}{\sin (\frac{π}{4}) - \cos (\frac{π}{4})}$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Subtract $\sqrt{2}$ from $\sqrt{2}$ .

$\frac{1 - \tan (\frac{π}{4})}{\frac{0}{2}}$

Step 2.3

Divide $0$ by $2$ .

$\frac{1 - \tan (\frac{π}{4})}{0}$

Step 2.4

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{1 - \tan (\frac{π}{4})}{0}$

Step 3

The expression contains a division by $0$ . The expression is undefined.

Undefined