# How do we simplify sintheta/sin(theta + pi/2)?

Mar 4, 2017

The expression equals $\tan \theta$.

#### Explanation:

We can expand the denominator using $\sin \left(A + B\right) = \sin A \cos B + \sin B \cos A$.

$\sin \frac{\theta}{\sin \theta \cos \left(\frac{\pi}{2}\right) + \sin \left(\frac{\pi}{2}\right) \cos \theta}$

sintheta/((0)sin theta + 1(costheta)

$\sin \frac{\theta}{\cos} \theta$

Use $\tan \theta = \sin \frac{\theta}{\cos} \theta$:

$\tan \theta$

Hopefully this helps!