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#1 2007-05-22 07:25:30
- nagy
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- 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
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- Registered: 2007-05-22
- Posts: 3
Re: trigonometry
George,Y wrote:
4sin20sin20sin40tan30
4sin20cos20cos40=4sin20sin20sin40tan30
sin80So 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 Ive cracked it.
The triple-angle formula for tan gives
(2)×(3) gives
Now multiply (4) and (1) and the result follows! Woot woot! 
Last edited by JaneFairfax (2007-05-23 08:23:27)
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