So there was an equation that I didn't quite understand, and I was hoping somebody could give me some insight. Here it goes...

Find ALL solutions to the equation: 3sintcost = 3cost

it was on mymathlab and the solution box was set up something like this: t = ____, where N is any integer.

the correct answer was: pi/2 + pi*N

my answer was: pi/2 + 2pi*N

*** I do not understand why it is "+ pi*N", because the sine and cosine functions have a periodicity of 2pi.

can someone explain why it is simply "+ pi*N" instead of "+ 2pi*N"??