Description for Correct answer:
By trigonometric identity,

\( \Large sec^{2} \theta -tan^{2} \theta =1 \)

=> \( \Large (sec \theta +tan \theta )(sec \theta -tan \theta )=1 \)

=> \( \Large sec \theta -tan \theta =\frac{1}{2} \) ....(i)

and given, \( \Large sec \theta +tan \theta =2 \) .....(ii)

On adding Eqs. (i) and (ii), we get

\( \Large 2sec \theta=\frac{1}{2}+2 \)

\( \Large sec \theta =\frac{5}{4} \)