Find the Exact Value sin(45 degrees )+cos(45 degrees )

$\sin (45 °) + \cos (45 °)$

Simplify each term.

The exact value of $\sin (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} + \cos (45 °)$

The exact value of $\cos (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{\sqrt{2} + \sqrt{2}}{2}$

Add $\sqrt{2}$ and $\sqrt{2}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

$\sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$