If secθ + tanθ = p, then what is the value of secθ – tanθ ?

Given that, sec θ + tan θ = p.

By trigonometric identity, we have

sec² θ – tan² θ = 1

So, sec² θ – tan² θ = 1

⇒ (sec θ – tan θ) (sec θ + tan θ) = 1

⇒ sec θ – tan θ = 1/(sec θ + tan θ)

⇒ sec θ – tan θ = 1/p [given]

Hence, sec θ – tan θ = 1/p.