Double-Angle, Power-Reducing, and Half-Angle Formulas Question?

Question

Half of an identity and the graph of this half are given. Use the graph to make a conjecture as to what the right side of the identity should be. Then prove your conjecture.

(cot x – tan x) / (cot x + tan x) = ?

http://i128.photobucket.com/albums/p168/thevampireambriz/Pre-Calculus/7JPG.jpg

Answer 1

(cot(x) - tan(x)) / (cot(x) + tan(x)) = cos(2x)

(cos(x) - sin^2(x)/cos(x)) / (cos(x) + sin^2(x)/cos(x)) = cos(2x)

(cos^2(x) - sin^2(x)) / (cos^2(x) + sin^2(x)) = cos(2x)

(cos^2(x) - sin^2(x)) = cos(2x)

cos(2x) = cos(2x)