- #1
Pawnag3
- 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