Question

If 5 tan θ = 4. then `(5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ)` = ______. 

Options

• 0

• 1

• `1/6`

• 6

Answer 1

If 5 tan θ = 4. then `(5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ)` = `bbunderline(1/6)`. 

Explanation:

5 tan 0 = 4 ⇒ tan 0 = `4/5`

∴ sin 0 = `4/sqrt41` and cos θ = `5/sqrt41`

`(5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ)`

`(5 × 4/sqrt41 − 3 × 5/sqrt41)/(5 × 4/sqrt41 + 2 × 5/sqrt41)`

= `1/6`