Evaluate -cos(pi/4)-sin(pi/4)

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

Simplify each term.

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

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

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

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

Simplify terms.

Combine the numerators over the common denominator.

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

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

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

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$- \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$