use a half angle identity to find the exact value of tan 45°

Question

use a half angle identity to find the exact value of tan 45°

Answer 1

Since this question asks us o use a half angle identity, step 1 is to look up the half angle identity for tangent.  There are at least two, so we'll just choose this one:

Tan (θ/2) = (1- Cos (θ)) / Sin (θ)

We want Tan (45)

So... 90/2 is 45... right?  That means θ needs to = 90.  Let's go back to our identity formula and substitute 90 for Theta (θ)

Tan (90/2) = (1 - Cos (90)) / Sin (90)

Now you need to either use a unit circle or calculator (depending on your teacher's preference) to find cos (90) and sin(90) and finish out the math.  (Yes, you should get the answer Kenneth S mentioned).

Answer 2

The answer is ONE that's because sin 45^o = cos 45^o and tan (90/2) might verify this if you care to go that (unnecessary) way!