# How do you simplify cos(x+pi/2)?

Use the known trigonometric identity

$\cos \left(a + b\right) = \cos a \cdot \cos b - \sin a \cdot \sin b$

we have that

$\cos \left(x + \frac{\pi}{2}\right) = \cos x \cdot \cos \left(\frac{\pi}{2}\right) - \sin x \cdot \sin \left(\frac{\pi}{2}\right) = \cos x \cdot 0 - \sin x \cdot 1 = - \sin x$

Finally

$\cos \left(x + \frac{\pi}{2}\right) = - \sin x$