1. The problem statement, all variables and given/known data Solve: 2 tan x (tan x - 1) = 3. 2. Relevant equations Pythagorean identities? 3. The attempt at a solution I tried the following: 2 tan^2 x - 2 tan x = 3 2 (sec^2 x - 1) - 2 tan x = 3 2 (1 - cos^2 x) - 2 sin x cos x = 3 cos^2 x (multiplying through by cos^2 x) ...but then I got confused (not wanting to write sin x = sqrt(1 - cos^2 x) and end up with an algebraic mess). Is there an easier way to solve the problem? Thanks!