Using your Head is Permitted

May 2011 riddle

UPDATE (3 May): It has been brought to my attention by several readers than one should, additionally, require n>1. The equation does not hold for n=1.

Prove the following trigonometric equality:

Note: You are permitted to look up basic trigonometric equalities in order to solve this riddle. You are not expected to have memorized these.

List of solvers:

Daniel Bitin (1 May 08:47)
Dan Dima (1 May 21:06)
Gaoyuan Chen (1 May 22:28)
Djinn Lu (1 May 22:57)
Jan Fricke (2 May 07:54)
Hu Han (3 May 12:20)
Lu Wang (4 May 00:52)
Harsha HS (4 May 17:02)
Albert Stadler (10 May 15:17)
Feifei Ji (13 May 02:21)
Zizhuo Wang (13 May 15:26)
Yan Wang (15 May 21:40)
Ganesh Lakshminarayana (24 May 03:38)
Sylvain Becker (24 May 03:51)
Joseph DeVincentis (24 May 23:31)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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