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Question: An multivariate inequality

Question:An multivariate inequality

pawanlri 4 Maple
August 01 2008
0

Hi to all,

I need to verify an multivariate equality in maple, here it goes:

Nr := 3 - cos(x - y) - cos( z - x) - cos(y - z);

Dr := (sin(x/2))^2 +  (sin(y/2))^2 + (sin(z/2))^2;

assume(x>0, x<Pi); assume(y>0,y<Pi); assume(z>0,z<Pi);

eqn := Nr/Dr;

I need to check whether eqn <= 6. I have tried

is(eqn > 6)  and is(eqn <=6) and both give FAIL as output. But if I change the denominator, Dr say Dr := Dr + 6;

and then I get the result true which is indeed true. but if I change Dr to Dr + 1 or Dr + 2 ... Dr + 5  maple gives FAIL

as output. Can anyone explain this or does anyone know another way to verify this inequality.?

Thanks in advance!

pawan

 
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