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Trigo inequality (Posted on 2014-12-11) Difficulty: 3 of 5
Let c be the Champernowne's constant, or c=0.123456789101112131415161718192021....

Show, without calculator aid, that
sin(c) + cos(c) + tan(c) > 10c

No Solution Yet Submitted by Danish Ahmed Khan    
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re(3): solution | Comment 7 of 11 |
(In reply to re(2): solution by Ady TZIDON)

Yes the only problem is that to get that .008 you needed to use a calculator.


An alternative would be to use two more terms of the Taylor series, perhaps with an easier to use number than Champernowne's: at x=1/8, the sum already exceed's 10 x Champernowne's number and is increasing; if that could be shown easily (p&p) with more Taylor terms, that would be good.

  Posted by Charlie on 2014-12-13 13:17:10
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