Tips for Solving Half Angle Identities with Horizontal Shifts

[dranseth]

Homework Statement

I'm on the last section of identities entitled half angle identities. This one seems to give me some trouble because I have never encountered one with a horizontal shift in it. Tips?

tan 1/2( ß + π/2 ) = ( 1 + sin ß ) / cos ß

 

[quantumdude]

Recall that:

$$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$$

Now, what do the graphs of the sine and cosine functions look like when you shift them to the left by $\frac{\pi}{2}$ rad?