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Derivation of Sum/Difference of Sine, Cosine, Tangent

Date: 02/16/2002 at 22:32:24
From: Meredith
Subject: Derivation of the Sum/Difference of Sine, Cosine, and Tangent

How can I find the derivation of the sum/difference of sine, cosine, 
and tangent?

Date: 02/17/2002 at 00:07:41
From: Doctor Schwa
Subject: Re: Derivation of the Sum/Difference of Sine, Cosine, and 

Hi Meredith,

A beautiful geometric approach is at

   Geometry of Addition and Subtraction Formulas - Smiley

and another approach, which I got from John Conway, is at

   Trig/Analyt Handouts - Joshua Zucker
   (select the link to "a derivation of the angle addition formula 
    for sine - PDF format)

A very nice exposition of the standard geometric proof is in our 

   Cosine Addition Formula

with a slightly different approach at

   Sine and Cosine Addition Formulas

There's also the derivation using complex numbers, which is
suggested at

   Trigonometric Functions and Euler's Identity

and made much more explicit at

   Euler's Formula

I hope at least one of those methods appeals to you.  Let me know
if you would like more information about any of them.  My favorites
are Conway's and the complex number method in that last link.

- Doctor Schwa, The Math Forum
Associated Topics:
High School Imaginary/Complex Numbers
High School Trigonometry

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