If Tan θ + Sec θ = a, then what is Sec θ equal to:

Correct option is D

Tan θ + Sec θ = a
Concept :
Tan θ + Sec θ = 1/Tan θ - Sec θ
Sec θ - Tan θ = 1/a ....(1)
Tan θ + Sec θ = a ...(2)
Solving both 1 and 2,
2 Sec θ = a + 1/a
2 Sec θ = (a² + 1)/a
Sec θ = (a² + 1)/2a