If sec θ + tan θ = x, find the value of sec θ.
Given: sec θ + tan θ = x ……(1)
Then, (sec θ + tan θ) × = x
⇒ = x
⇒ = x
⇒ sec θ – tan θ = (1/x) ……(2)
Adding equation (1) and (2), we get:
2 sec θ = x + (1/x)
= (x2 + 1)/x
⇒ sec θ = (x2 + 1)/2x
Therefore, sec θ = (x2 + 1)/2x