When dealing with trig identities, you don't have to memorize the double angle formulas.

If you know sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
                   cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

you can get

sin(2a) = sin(a + a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a)

That's how the double angle identities are derived.

cos(2a) =  cos(a + a) = cos(a)cos(a) - sin(a)sin(a) = cos^2(a) - sin^2(a)

The same holds true for tan(a + b), you can derive tan(2a) = tan(a + a).