Trigonometry Examples

$\sin (2 x) - \cos (2 x)$

Step 1

Apply the sine double-angle identity.

$2 \sin (x) \cos (x) - \cos (2 x)$

Step 2

Use the double-angle identity to transform $\cos (2 x)$ to $1 - 2 \sin^{2} (x)$ .

$2 \sin (x) \cos (x) - (1 - 2 \sin^{2} (x))$

Step 3

Apply the distributive property.

$2 \sin (x) \cos (x) - 1 \cdot 1 - (- 2 \sin^{2} (x))$

Step 4

Multiply $- 1$ by $1$ .

$2 \sin (x) \cos (x) - 1 - (- 2 \sin^{2} (x))$

Step 5

Multiply $- 2$ by $- 1$ .

$2 \sin (x) \cos (x) - 1 + 2 \sin^{2} (x)$