- #1

- 12

- 0

## 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