Question

If `tan θ = sqrt(3)` then sec θ = ?

Options

• 2

• `1/2`

• `sqrt(3)/2`

• `2/sqrt(3)`

Answer 1

2

Explanation:

`tan θ = sqrt(3)`

⇒ `(BC)/(AB) = sqrt(3)/1`

Let `BC = sqrt(3)k` and AB = k. Then,

AC² = (AB² + BC²)

= (k² + 3k²)

= 4k²

⇒ `AC = sqrt(4k^2)`

⇒ AC = 2k

∴ `sec θ = (AC)/(AB)`

= `(2k)/k`

= 2