Trigonometry Examples

$\frac{1}{2} \cdot (\cos (8 x - 4 x) - \cos (8 x + 4 x))$

Step 1

Simplify each term.

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Step 1.1

Subtract

$4 x$ from

$8 x$ .

$\frac{1}{2} \cdot (\cos (4 x) - \cos (8 x + 4 x))$

Step 1.2

Add

$8 x$ and

$4 x$ .

$\frac{1}{2} \cdot (\cos (4 x) - \cos (12 x))$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$\frac{1}{2} \cos (4 x) + \frac{1}{2} (- \cos (12 x))$

Step 2.2

Combine

$\frac{1}{2}$ and

$\cos (4 x)$ .

$\frac{\cos (4 x)}{2} + \frac{1}{2} (- \cos (12 x))$

Step 2.3

Combine

$\frac{1}{2}$ and

$\cos (12 x)$ .

$\frac{\cos (4 x)}{2} - \frac{\cos (12 x)}{2}$