Question

If `cos θ = 4/5` then tan θ = ?

Options

• `3/4`

• `4/3`

• `3/5`

• `5/3`

Answer 1

`bb(3/4)`

Explanation:

`cos θ = 4/5`

⇒ `(AB)/(AC) = 4/5`

Let AB = 4k and AC = 5k. Then,

BC² = (AC² – AB²) 

= (25k² – 16k²) 

= 9k²

⇒ `BC = sqrt(9k^2)`

⇒ BC = 3k.

∴ `tan θ = (BC)/(AB)`

= `(3k)/(4k)`

= `3/4`