Precalculus Examples

$2 \sin (\frac{10 - 50}{2}) \cos (\frac{10 + 50}{2})$

Step 1

Cancel the common factor of $10 - 50$ and $2$ .

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Step 1.1

Factor $2$ out of $10$ .

$2 \sin (\frac{2 \cdot 5 - 50}{2}) \cos (\frac{10 + 50}{2})$

Step 1.2

Factor $2$ out of $- 50$ .

$2 \sin (\frac{2 \cdot 5 + 2 \cdot - 25}{2}) \cos (\frac{10 + 50}{2})$

Step 1.3

Factor $2$ out of $2 \cdot 5 + 2 \cdot - 25$ .

$2 \sin (\frac{2 \cdot (5 - 25)}{2}) \cos (\frac{10 + 50}{2})$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $2$ .

$2 \sin (\frac{2 \cdot (5 - 25)}{2 (1)}) \cos (\frac{10 + 50}{2})$

Step 1.4.2

Cancel the common factor.

$2 \sin (\frac{2 \cdot (5 - 25)}{2 \cdot 1}) \cos (\frac{10 + 50}{2})$

Step 1.4.3

Rewrite the expression.

$2 \sin (\frac{5 - 25}{1}) \cos (\frac{10 + 50}{2})$

Step 1.4.4

Divide $5 - 25$ by $1$ .

$2 \sin (5 - 25) \cos (\frac{10 + 50}{2})$

Step 2

Subtract $25$ from $5$ .

$2 \sin (- 20) \cos (\frac{10 + 50}{2})$

Step 3

Cancel the common factor of $10 + 50$ and $2$ .

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Step 3.1

Factor $2$ out of $10$ .

$2 \sin (- 20) \cos (\frac{2 \cdot 5 + 50}{2})$

Step 3.2

Factor $2$ out of $50$ .

$2 \sin (- 20) \cos (\frac{2 \cdot 5 + 2 \cdot 25}{2})$

Step 3.3

Factor $2$ out of $2 \cdot 5 + 2 \cdot 25$ .

$2 \sin (- 20) \cos (\frac{2 \cdot (5 + 25)}{2})$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$2 \sin (- 20) \cos (\frac{2 \cdot (5 + 25)}{2 (1)})$

Step 3.4.2

Cancel the common factor.

$2 \sin (- 20) \cos (\frac{2 \cdot (5 + 25)}{2 \cdot 1})$

Step 3.4.3

Rewrite the expression.

$2 \sin (- 20) \cos (\frac{5 + 25}{1})$

Step 3.4.4

Divide $5 + 25$ by $1$ .

$2 \sin (- 20) \cos (5 + 25)$

Step 4

Add $5$ and $25$ .

$2 \sin (- 20) \cos (30)$

Step 5

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

$2 \sin (- 20) \frac{\sqrt{3}}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $2 \sin (- 20)$ .

$2 (\sin (- 20)) \frac{\sqrt{3}}{2}$

Step 6.2

Cancel the common factor.

$2 \sin (- 20) \frac{\sqrt{3}}{2}$

Step 6.3

Rewrite the expression.

$\sin (- 20) \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sin (- 20) \sqrt{3}$

Decimal Form:

$- 0.59239626 \dots$