direction cosines/vector help

Hi everyone! I'm working on a vector question involving finding and proving direction cosines/sines/tangents of vector (a,b,c), u = magnitude

I know:

cos[alpha] = a/u, cos[beta] = b/u, cos[gamma] = c/u, and that cos2[alpha] + cos2[beta] + cos2[gamma] = 1 (the 2s are squares). But I don't understand the second part. I know it must be pretty simple and related to unit vectors, and I'm just missing something, so any help would be very much appreciated! Also, any help on the sine/tangent part would be useful, too.

Thanks so much for any and all help!