Question

Is Cos 15` A Rational Number?

Answer 1

No it is not 
Cos15=Cos(45-30)
             Cos45.Cos30 + Sin45.Sin30   (cos(a-b)=cosa.cosb+sina.sinb)
              Now put the values and u will find that it is irrational
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Answer 2

No, 
Because
cos 15 = cos 60 - cos 45.
and cos 45 is irrational.
and you know that the sum of irrational and rational number is irrational