Question

If cosec θ = `sqrt(10)` then sec θ = ?

Options

• `1/sqrt(10)`

• `2/sqrt(10)`

• `3/sqrt(10)`

• `sqrt(10)/3`

Answer 1

`bb(sqrt(10)/3)`

Explanation:

cosec θ = `sqrt(10)`

⇒ `sin θ = 1/sqrt(10) = (BC)/(AC)`.

Let BC = k and `AC = sqrt(10)k`.

AB² = (AC² – BC)²) 

= (10k² – k²) 

= 9k²

∴ `AB = sqrt(9k^2)`

= 3k

∴ `sec θ = (AC)/(AB)`

= `(sqrt(10)k)/(3k)`

= `sqrt(10)/3`