+129852 Yes, xvxvxv, e is correct for the second question.
As to your hypothesis...let's see if this it is true that cos(n*pi + x) = cos(x)
Using a trig identity, we have
cos(n*pi + x) =
cos(n*pi)cos(x) - sin(n*pi)sinx =
cos(n*pi)cos(x)
Notice that this equals cos(x) only when n = 0, 2, 4, 6......
+1832 nice alan .. so question 2 the answer is e ! right ?
and I want to ask ... from your amswer in question 6 I Concluded this law 
cos(npi + x ) = cos(x) ... n mean any Integer number ( 0 , 1 , 2 , 3 ....... )
+129852 Yes, xvxvxv, e is correct for the second question.
As to your hypothesis...let's see if this it is true that cos(n*pi + x) = cos(x)
Using a trig identity, we have
cos(n*pi + x) =
cos(n*pi)cos(x) - sin(n*pi)sinx =
cos(n*pi)cos(x)
Notice that this equals cos(x) only when n = 0, 2, 4, 6......
