Explanation:
In these types of problems, you need to use various trigonometric identities to solve this.
First, note what are you trying to solve.
We are trying to find

Using our trig identities, we know that

Next, in order to solve this problem, we need to find cos(alpha).
So using our given info, of tan(alpha), we must find a way to manipulate that information to get cos(alpha)
Notice that


And that

So,

Using the interval, since cos is negative over the interval (pi,3pi/2),
our answer will be negative

We know that

So




Since we know what cos(alpha) is, We can solve cos(alpha/2), likewise, cos will be negative since the former is negative over pi and 3pi/2




