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

[cmkluza]

Homework Statement

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

Homework Equations

cot(θ) = (1 + cos(2θ)) / sin(2θ)

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!

 

[Dick]

Homework Statement

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

Homework Equations

cot(θ) = (1 + cos(2θ)) / sin(2θ)

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!

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".

 

[SammyS]

Homework Statement

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

Homework Equations

cot(θ) = (1 + cos(2θ)) / sin(2θ)

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!

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

 

[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

 

[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.

 

[Mark44]

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

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.