Expand the Trigonometric Expression sin(x-pi/4)

$\sin (x - \frac{π}{4})$

Step 1

Apply the difference of angles identity.

$\sin (x) \cos (\frac{π}{4}) - \cos (x) \sin (\frac{π}{4})$

Step 2

Simplify each term.

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\sin (x) \frac{\sqrt{2}}{2} - \cos (x) \sin (\frac{π}{4})$

Combine $\sin (x)$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\sin (x) \sqrt{2}}{2} - \cos (x) \sin (\frac{π}{4})$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sin (x) \sqrt{2}}{2} - \cos (x) \frac{\sqrt{2}}{2}$

Combine $\frac{\sqrt{2}}{2}$ and $\cos (x)$ .

$\frac{\sin (x) \sqrt{2}}{2} - \frac{\sqrt{2} \cos (x)}{2}$