Proof of Tangent Double Angle IdentityDate: 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/ |
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