# Thread: Trigonometric Identity Problem

1. ## Trigonometric Identity Problem

This is probably pretty simple, I cant figure it out though.

"Prove the identity (T = Theta): (cos(2T)) / (1 + sin(2T)) = (cot(T) - 1) / (cot(T) + 1)"

So...
((cos(T)^2) - (sin(T)^2)) / (1 + 2*sin(T)*cos(T)) = (cos(T) - sin(T)) / (cos(T) + sin(T))

(cos(T) + sin(T)) * ((cos(T)^2) - (sin(T)^2)) = (cos(T) - sin(T)) * (1 + 2*sin(T)*cos(T))

(cos(T) + sin(T)) * (cos(T) - sin(T)) = (1 + 2*sin(T)*cos(T))

((cos(T)^2) - (sin(T)^2)) = (1 + 2*sin(T)*cos(T))

At this point I am stuck. What do I need to do now?

2. Here.

3. $\frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cot{t} - 1}{\cot{t} + 1}$

multiply the right side by $\frac{\sin{t}}{\sin{t}}$ ...

$\frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos{t} - \sin{t}}{\cos{t} + \sin{t}}$

multiply right side by $\frac{\cos{t} + \sin{t}}{\cos{t} + \sin{t}}$ ...

$\frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos^2{t} - \sin^2{t}}{\cos^2{t} + 2\sin{t}\cos{t} + \sin^2{t}}$

$\frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos(2t)}{1 + \sin(2t)}$