The numerical value of $$\frac{5}{{{\text{se}}{{\text{c}}^2}\theta }}$$  + $$\frac{2}{{1 + {\text{co}}{{\text{t}}^2}\theta }}$$  + $${\text{3}}{\sin ^2}\theta $$   is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{5}{{{\text{se}}{{\text{c}}^2}\theta }}{\text{ + }}\frac{2}{{1 + {\text{co}}{{\text{t}}^2}\theta }}{\text{ + 3}}{\sin ^2}\theta \cr & = 5{\cos ^2}\theta + \frac{2}{{{\text{cose}}{{\text{c}}^2}\theta }} + 3{\sin ^2}\theta \cr & = 5{\text{co}}{{\text{s}}^2}\theta + 2{\sin ^2}\theta + 3{\sin ^2}\theta \cr & = 5\left( {{\text{co}}{{\text{s}}^2}\theta + {{\sin }^2}\theta } \right) \cr & \left( {\because {{\sin }^2}\theta + {\text{co}}{{\text{s}}^2}\theta = 1} \right) \cr & = 5 \times 1 \cr & = 5 \cr} $$