Trigonometric Proof

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MCP12
Posts: 1
Joined: Sat Jan 12, 2013 9:27 am

Trigonometric Proof

Unread post by MCP12 » Sat Jan 12, 2013 6:38 pm

Hello! This is my first post on this wonderful forum, and I hope one of many more to come.

Here is the first question to be posed:

Prove, in as elegant a manner as possible, that
\[\sin x = 2^n \cdot \cos \frac {x}{2} \cdot \cos \frac{x}{x^2} \cdot \cdot \cdot \cos \frac {x}{2^n} \cdot \sin \frac{x}{2^n} \].

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zadid xcalibured
Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

Re: Trigonometric Proof

Unread post by zadid xcalibured » Sat Jan 12, 2013 10:53 pm

Repeated use of the identity $Sin(2x)=2sin(x).cos(x)$
There can be no more elegant proof.

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