The correct option is B 19
Here, AB is perpendicular(P), BC is base(B) and AC is hypotenuse(H).
BC=√AC2−AB2=√10−1=3
∴sinθ=PH=1√10
⇒cosecθ=√10 ...(i)
Also, tanθ=PB=13
⇒cotθ=3 ...(ii)
On squaring and adding (i) and (ii), we get
cosec2θ+cot2θ=10+9=19
Option B is correct.