Prove that

Posted July 6th, 2009 by alpha

Prove that
$tan20^0tan40^0tan60^0tan80^0=3$

Comments

On July 7th, 2009 Structure says:

$8\sin 20 \sin40\sin80=4 \sin 20(\cos 40-\cos 120)=4\sin 20(\cos40+\cos60)=$

$=4 \sin 20\cos 40+4\sin 20\cos 60=2\sin 60 -2 sin 20+2 sin 20=\sqrt3$

$\sin 20=\sin160=2 \sin 80 \cos 80=4\sin40\cos 40 \cos 80=8\sin 20 \cos 20 \cos 40\cos 80$

$1=8\cos 20 \cos 40\cos 80$

On July 8th, 2009 alpha says:

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``Old theorems never die; they turn into definitions.''
----E. Hewitt

''ALPHA" =)