If sec θ + tan θ = x, then tan θ =
Given: sec θ + tan θ = x ……………(i)
To find: tan 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)
Subtracting (ii) from (i), we get