Solve tan2A - 2tanA = -1 for 0º≤A≤360º.

Answer 1

remember your double-angle formula

tan2A = 2tanA/(1-tan^2 A)

so,

2tanA/(1-tan^2 A) - 2tanA = -1
2tanA * tan^2 A = tan^2 A - 1
2tan^3 A - tan^2 A + 1 = 0

Hmmm. Nasty. You need to solve

2x^3 - x^2 + 1 = 0

and then take the arctan of whatever solution you find.