If sec θ + tan θ = x, find the value of sec θ.

Question

Philoid · Accepted Answer

Given: sec θ + tan θ = x ……(1)

Then, (sec θ + tan θ) × = 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