They are only true if a=45
Proof (Using degrees):
sin(45) = cos(45)
Test:
a = 45
sin(4*45)-cos(4*45) = 1
sin(2*45)-cos(2*45) = 1
sin(90) = 1
cos(90) = 0
sin(180) = 0
cos(180) = -1
1-0 = 1
0-(-1) = 0+1 = 1
I cannot give you a formula, but this is just an easy way to give a small proof.
You might have had already your test, but it's good to know afterwards too.