1. The problem statement, all variables and given/known data Basically, solve for x 15 = arctan(2/x) - arctan (1/x) 2. Relevant equations tan (A-B) = (Tan A -Tan B) / (1+Tan A*Tan B) 3. 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
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!
If you rearrange that equation you'll get the quadratic [tex]x^2-\frac{1}{tan(15)}x+2=0[/tex] There are no real solutions to this quadratic.