Basic Math Examples

$\frac{\sin (30)}{\cos (60)} + \frac{\sin (45)}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{\frac{1}{2}}{\cos (60)} + \frac{\sin (45)}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1.2

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

$\frac{\frac{1}{2}}{\frac{1}{2}} + \frac{\sin (45)}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1.3

Cancel the common factor of $\frac{1}{2}$ .

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Step 1.3.1

Cancel the common factor.

$\frac{\frac{1}{2}}{\frac{1}{2}} + \frac{\sin (45)}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1.3.2

Rewrite the expression.

$1 + \frac{\sin (45)}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1.4

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

$1 + \frac{\frac{\sqrt{2}}{2}}{\cos (45)} \cdot \frac{\cos (30)}{1} - 2 \cos (60)$

Step 1.5

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

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

Step 1.6

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

$1 + \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \cdot \frac{\frac{\sqrt{3}}{2}}{1} - 2 \cos (60)$

Step 1.7

Cancel the common factor of $\frac{\sqrt{2}}{2}$ .

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Step 1.7.1

Cancel the common factor.

$1 + \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \cdot \frac{\frac{\sqrt{3}}{2}}{1} - 2 \cos (60)$

Step 1.7.2

Rewrite the expression.

$1 + 1 \cdot \frac{\frac{\sqrt{3}}{2}}{1} - 2 \cos (60)$

Step 1.8

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

$1 + \frac{\frac{\sqrt{3}}{2}}{1} - 2 \cos (60)$

Step 1.9

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

$1 + \frac{\sqrt{3}}{2} - 2 \cos (60)$

Step 1.10

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

$1 + \frac{\sqrt{3}}{2} - 2 (\frac{1}{2})$

Step 1.11

Cancel the common factor of $2$ .

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Step 1.11.1

Factor $2$ out of $- 2$ .

$1 + \frac{\sqrt{3}}{2} + 2 (- 1) \frac{1}{2}$

Step 1.11.2

Cancel the common factor.

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

Step 1.11.3

Rewrite the expression.

$1 + \frac{\sqrt{3}}{2} - 1$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $1$ from $1$ .

$0 + \frac{\sqrt{3}}{2}$

Step 2.2

Add $0$ and $\frac{\sqrt{3}}{2}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$