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