Question

If sec θ - tan θ = m, then the value of sec θ + tan θ is ______.

Options

• `1 - 1/m`

• `m^2 - 1`

• `1/m`

• -m

Answer 1

If sec θ - tan θ = m, then the value of sec θ + tan θ is `underline(1/m)`.

Explanation:

Given,

sec θ - tan θ = m     ...(i)

We know that, sec²θ - tan²θ = 1

⇒ (sec θ - tan θ) (sec θ + tan θ) = 1

⇒ sec θ + tan θ = `1/(secθ - tanθ)`

⇒ sec θ + tan θ = `1/m`    ...[from (i)]