# Angle Help!15 = arctan(2/x) - arctan (1/x)

Pawnag3

## Homework Statement

Basically, solve for x
15 = arctan(2/x) - arctan (1/x)

## Homework Equations

tan (A-B) = (Tan A -Tan B) / (1+Tan A*Tan B)

## The Attempt at a Solution

I really tried everything.
My first step was to:
Let y = arctan (2/x)
Therefore, tan y = 2/x
Similarly, u = 1/x
Then, tan (y-u) = (Tan y -Tan u) / (1+Tan u*Tan y) = 15
15 = (2/x-(1/x) / (1+(2/x^2)
15 = (1/x) / (x^2 + 2 / x^2)
15 = (x) / (x^2+2)
15x^2 + 30 - x = 0
Which has no real roots :(
But, with guess and check, it's around 0.65

Homework Helper
You need to post an attempt before we can help you. Start by taking the tangent of both sides.

Pawnag3
Yeah, sorry. I just misclicked the first time

Pawnag3
Alright, sorry guys to waste your time, but I believe I figured it out. Thanks for the hint of "tanning" both sides.
Instead of 15, it's supposed to be tan 15.
So that,
x/(x^2+2) = tan 15
x = 0.64
x = 3.08 (approximately)

Thanks for the help!

Homework Helper
If you rearrange that equation you'll get the quadratic

$$x^2-\frac{1}{tan(15)}x+2=0$$

There are no real solutions to this quadratic.