If sec θ + tan θ = 2, then sec θ is equal to:

Correct option is A

Given:

​$$\sec \theta + \tan \theta = 2$$​​
Formula Used:
​$$\sec^2 \theta - \tan^2 \theta = 1$$​​
Solution:
​$$\sec \theta + \tan \theta = 2 \quad \text{(1)}$$​​

​$$\sec^2 \theta - \tan^2 \theta = 1 \\ \ \\(\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1 \\ \ \\\sec \theta - \tan \theta = \frac{1}{2} \quad \text{(2)} \\ \ \\\text{Add equations (1) and (2)}: (\sec \theta + \tan \theta) + (\sec \theta - \tan \theta) = 2 + \frac{1}{2} \\ \ \\2 \sec \theta = \frac{5}{2} \\ \ \\\sec \theta = \frac{5}{4}$$​​