If 1 + cot²θ = $$\frac{{625}}{{49}}$$ and θ is acute, then what is the value of $${\left( {\sin \theta + \cos \theta } \right)^{\frac{1}{2}}}?$$

Solution(By Examveda Team)

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