If sinθ = 12/13 and θ is acute, the value of cosecθ + cotθ is:

cosθ = √(1 − 144/169) = 5/13, so cosecθ = 13/12 and cotθ = 5/12. Their sum is 18/12 = 3/2. (13/12 is only the first term; 18/13 comes from adding over the wrong denominator.)