Question

If sec θ – tan θ = 2, then sec θ + tan θ is equal to ______.

Options

• `1/2`

• `sqrt(2)`

• `1/sqrt(2)`

• 2

Answer 1

If sec θ – tan θ = 2, then sec θ + tan θ is equal to `underlinebb(1/2)`.

Explanation:

sec θ – tan θ = 2

Multiply both sides by (sec θ + tan θ).

⇒ (sec θ – tan θ) (sec θ + tan θ) = 2(sec θ + tan θ)

⇒ sec² θ – tan² θ = 2(sec θ + tan θ)   ...(∵ sec² θ – tan² θ = 1)

⇒ 1 = 2(sec θ + tan θ)

⇒ sec θ + tan θ = `1/2`