Proof of Tangent Double Angle Identity

Date: 7/16/96 at 16:6:35
From: Anonymous
Subject: Proof of Tangent Double Angle Identity

The proof for the double angle idenity of tangent is set in terms of 
sin and cos. I would think that the proof is possible using TAN 
(A + A) and without using the TAN(A + B) form. All of my attempts 
yield either " 2(sin cos) " or 2 Sin. Neither of these is correct. I 
would like to see the proof worked out, competely, with all but the 
most fundamental steps included.

Date: 7/16/96 at 22:46:38
From: Doctor Robert
Subject: Re: Proof of Tangent Double Angle Identity

I'm not sure that I understand your question, but here is the answer I 
think that you're asking for:

tan 2A = Sin 2A/Cos 2A = 2sinAcosA/((cosA)^2 - (sinA)^2)

Now, divide the numerator and the denominator of this fraction by 
(cosA)^2.

You get   
[2 sinA/cosA]/[1 - (sinA)^2/(cosA)^2]=2tanA/[1-(tanA)^2]
which is the formula for the tangent of a double angle. 

I hope this helps.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/