If 1 + cot2θ = 62549 and θ is acute, then what is the value of ( + )^1/2?

Answer: Option C

$$\begin{array}{rl}& 1+{\cot }^2\theta =\frac{625}{49}\\ & \text{cose}{\text{c}}^2\theta =\frac{625}{49}\\ & \text{cosec}\theta =\frac{25}{7}\\ & \sin \theta =\frac{7}{25}\\ & \cos \theta =\frac{24}{25}\\ & {\left(\sin \theta +\cos \theta \right)}^{\frac{1}{2}}\\ & ={\left(\frac{7}{25}+\frac{24}{25}\right)}^{\frac{1}{2}}\\ & ={\left(\frac{31}{25}\right)}^{\frac{1}{2}}\\ & =\frac{\sqrt{31}}{5}\end{array}$$