# Finding the Value of cot(pi/8) in the form a + b*sqrt(2)

1. Apr 9, 2015

### cmkluza

1. The problem statement, all variables and given/known data
Show that sin(2θ) / (1 + cos(2θ) = tan(θ) - I've completed this part
Hence find the value of cot(π/8) in the form a + b√(2), where a, b ∈ ℤ
2. Relevant equations
cot(θ) = (1 + cos(2θ)) / sin(2θ)

3. The attempt at a solution
I did the math, got (1 + cos(π/4)) / sin(π/4) = (1 + 1/2√(2)) / (1/2√(2)) = (2 + √(2)) / √(2) = (2 / √(2)) + 1
Assuming I did all the math correctly, I can't figure out how to get to a + b√(2) from here.
Any tips?

(Also if anyone can answer this, how can I make my math look more "math-like" in these forums? I hate having to insert math as typed up stuff that looks sloppy)

Thanks very much for any help anyone can offer!

2. Apr 9, 2015

### Dick

Isn't $\frac{2}{\sqrt{2}}=\sqrt{2}$? I'll try and find a link to a TeX tutorial on the website to help you make your stuff look more "math-like".

3. Apr 9, 2015

### SammyS

Staff Emeritus
Write $\displaystyle\ \frac{1+\cos(2\theta)}{\sin(2\theta)}\$ as $\displaystyle\ \frac{1}{\sin(2\theta)}+\frac{\cos(2\theta)}{\sin(2\theta)}\$ .

(Use LaTeX for math-like stuff.) LaTeX Guide

4. Apr 9, 2015

### deedsy

your math is correct, you can write it as $1 + \sqrt{2}$

a=b=1

To write math equations write the word "itex" in [], and when you're done write "itex" after the dash in [ /]
there may be a shortcut to that, though

5. Apr 9, 2015

### cmkluza

Thank you very much for your help! I should've considered rearranging the problem in the first place to get that answer, but I guess I just wasn't thinking of it at the time. It always bug me when I miss one small thing that could lead me to the answer. Also, thanks for introducing me to LaTeX! I'm going to have to look more into that.

6. Apr 10, 2015

### Staff: Mentor

There is a shortcut that I find easier to type. Instead of itex tags, use a ## pair at the beginning and another pair at the end. Use those for inline math stuff.

For standalone math stuff use a pair of  at the start and another pair at the end. These are equivalent to the [ tex ] and [ /tex ] tags.