Trigonometry Examples

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

Step 1

Simplify each term.

Tap for more steps...

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.

Tap for more steps...

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 $\cos (12 x)$ .

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