that's erh... 'obvious', it's something you should remember
some 'reasons':
1.) cotangent means complementary tangent, since (pi/2 - t) and t are complimentary (adds up to 90), you have that identity
2.)
tan (Pi/2 - t)
= sin(pi/2 - t)/cos(pi/2 -t)
= cos(t)/sin(t)
= cot(t)