If sec θ + tan θ = x, then sec θ =

Given: sec θ + tan θ = x ……………(i)

To find: sec θ

We know that 1 + tan² θ = sec² θ

⇒ sec² θ – tan² θ = 1

∵ a² – b² = (a – b) (a + b)

∴ sec² θ – tan² θ = (sec θ – tan θ) (sec θ + tan θ) = 1

⇒ From (i), we have

⇒ (sec θ – tan θ) x = 1

…………………(ii)

Adding (i) and (ii), we get