Question

If 4 tan θ = 3, then is equal to `(4 sin - cos θ)/(4 sin θ + cos θ)` is equal to ______.

Answer 1

If 4 tan θ = 3, then is equal to `(4 sin - cos θ)/(4 sin θ + cos θ)` is equal to `underlinebb(1/2)`.

Explanation:

4 tan θ = 3

⇒ `tan θ = 3/4`

`(4 sin θ - cos θ)/(4 sin θ + cos θ) = (4(sin θ/cos θ) - 1)/(4(sin θ/cos θ) + 1)`

= `(4 tan θ - 1)/(4 tan θ + 1)` 

= `(4 xx (3/4) - 1)/(4 xx (3/4) + 1)` 

= `(3 - 1)/(3 + 1)`

= `2/4`

= `1/2`