Precalculus Examples

$\cos (60) \cdot \cos (30) + \sin (60) \cdot \sin (30)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$\frac{1}{2} \cdot \cos (30) + \sin (60) \cdot \sin (30)$

Step 1.2

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{1}{2} \cdot \frac{\sqrt{3}}{2} + \sin (60) \cdot \sin (30)$

Step 1.3

Multiply $\frac{1}{2} \cdot \frac{\sqrt{3}}{2}$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2 \cdot 2} + \sin (60) \cdot \sin (30)$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{\sqrt{3}}{4} + \sin (60) \cdot \sin (30)$

Step 1.4

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{2} \cdot \sin (30)$

Step 1.5

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{2} \cdot \frac{1}{2}$

Step 1.6

Multiply $\frac{\sqrt{3}}{2} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 1.6.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{2}$ .

$\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{2 \cdot 2}$

Step 1.6.2

Multiply $2$ by $2$ .

$\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{4}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{\sqrt{3} + \sqrt{3}}{4}$

Step 2.2

Add $\sqrt{3}$ and $\sqrt{3}$ .

$\frac{2 \sqrt{3}}{4}$

Step 2.3

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $2 \sqrt{3}$ .

$\frac{2 (\sqrt{3})}{4}$

Step 2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.2.1

Factor $2$ out of $4$ .

$\frac{2 \sqrt{3}}{2 \cdot 2}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 \sqrt{3}}{2 \cdot 2}$

Step 2.3.2.3

Rewrite the expression.

$\frac{\sqrt{3}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$