Let's call "0" = t for convenience.

tan(t) + cot(t) = sin(t)/cos(t) + cos(t)/sin(t) <-- Get a common denominator then add the fractions:

= [sin^2(t) + cos^2(t)]/[sin(t)cos(t)]

= 1/[sin(t)cos(t)]

We can work with this a bit more:

= 2/[2sin(t)cos(t)] = 2/sin(2t) = 2*csc(2t)

-Dan

TECHNICAL COMMENT: Tan(t) and tan(t) are technically two different functions. The correct usage for the common trig functions is sin(t), cos(t), tan(t), csc(t), sec(t), and cot(t).