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### Proof of Tangent Double Angle Identity

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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

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/
```
Associated Topics:
High School Calculus

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