Question

If sec θ + tan θ = k, then sec θ − tan θ is equal to ______.

Options

• 1

• `1/k`

• 0

• 1 − k

Answer 1

If sec θ + tan θ = k, then sec θ − tan θ is equal to `bbunderline(1/k)`.

Explanation:

sec² θ − tan² θ = 1

(sec θ + tan θ)(sec θ − tan θ) = 1

We are given that sec θ + tan θ = k.

 Substitute this into the equation:

(k)(sec θ − tan θ) = 1

Divide both sides by k:

sec θ − tan θ = `1/k`