That identity is at the start (page 1, line 1) of one of the true great math books, Mark Kac's Statistical Independence in Prob., Analysis and Number tTheory. He attributes it to Vieta. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Fri, Apr 17, 2015 at 11:05 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
sin(x) = 2 cos(x/2) sin(x/2) = 4 cos(x/2) cos(x/4) sin(x/4) = 2^n cos(x/2) ... cos(x/2^n) sin(x/2^n). In the limit, 2^n sin(x/2^n) = x. -- Gene
From: David Wilson <davidwwilson@comcast.net> To: 'math-fun' <math-fun@mailman.xmission.com> Sent: Thursday, April 16, 2015 8:23 PM Subject: [math-fun] What's the proof?
x*cos(x/2)*cos(x/4)*cos(x/8)*. = sin(x).
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