Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

Factor $2$ out of $- 2 \sqrt{2}$ .

$\frac{2 (- \sqrt{2})}{2}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $2$ .

$\frac{2 (- \sqrt{2})}{2 (1)}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 (- \sqrt{2})}{2 \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

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

Step 2.3.2.4

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

$- \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$