trig
posted by trig .
Solve tan2A  2tanA = 1 for 0º≤A≤360º.

Hmmm. Sensing a missing ^ character, we have
tan^2(A)  2tanA + 1 = 0
(tanA  1)^2 = 0
tanA = 1
So, A = 45º or 225º 
or taking it at face value the way it was typed
tan 2A  2tan A = 1
2tanA/(1tan^2 A)  2tanA = 1
let tanA = x for easier typing
2x/(1x^2)  2x = 1
times 1  x^2
2x  2x + 2x^3 = 1 + x^2
2x^3  x^2 + 1 = 0
by Wolfram
http://www.wolframalpha.com/input/?i=2x%5E3++x%5E2%2B1%3D0
x = .657298
tanA = .657298
A = 146.7° or A = 326.7°
both work 
a ladder leaning against a vertical wall make an angle 24 degrees with the wall.the foot of the ladder is 5 ft from the wall find the length of the ladder

You lean a ladder 6.7 m long against a wall. It makes an angle of 63 degrees with the level ground. How high up is the top of the ladder?