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#1 2007-05-22 07:25:30

nagy
Member
Registered: 2007-05-22
Posts: 0

trigonometry

Without using calculator , Prove that
(tan20°)×(tan30°)×(tan40°)= (tan10°)

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#2 2007-05-22 12:06:14

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: trigonometry

4sin20sin20sin40tan30
4sin20cos20cos40

=4sin20sin20sin40tan30
               sin80

So  4sin20sin20sin40tan30 should be sin10


X'(y-Xβ)=0

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#3 2007-05-22 20:32:28

lancemaria
Member
Registered: 2007-05-22
Posts: 3

Re: trigonometry

George,Y wrote:

4sin20sin20sin40tan30
4sin20cos20cos40

=4sin20sin20sin40tan30
               sin80

So  4sin20sin20sin40tan30 should be sin10

is this correct?

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#4 2007-05-23 05:59:50

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: trigonometry

I think I’ve cracked it.

The triple-angle formula for tan gives

(2)×(3) gives

Now multiply (4) and (1) and the result follows! Woot woot! jumping-smiley-017.gif

Last edited by JaneFairfax (2007-05-23 08:23:27)

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