If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.

Question

Philoid · Accepted Answer

Given: sec θ + tan θ = x ……………(i)

To find: sec θ – tan θ

We know that 1 + tan² θ = sec² θ

⇒ 1 = sec² θ – tan² θ

Now, ∵ a² – b² = (a – b) (a + b)

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

⇒ From (i), we have

1 = (sec θ – tan θ) x