Question

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

Answer 1

Given:` secθ+tanθ=x` 

We know that, 

`Sec^2θ-tan^2θ=1` 

Therefore, 

`sec^2 θ-tan^2θ=1` 

⇒` (Secθ+tan θ) (Secθ-tan θ)=1` 

⇒` x (secθ-tan θ )=1` 

⇒ `(sec θ-tan θ)=1/x` 

Hence, `sec θ-tan θ=1/4`