Question

If sin θ = 2 cos θ, then `(3 sin θ - cos θ)/(3 sin θ + cos θ)` is equal to ______.

Options

• 0

• `1/2`

• `2/5`

• `5/7`

Answer 1

If sin θ = 2 cos θ, then `(3 sin θ - cos θ)/(3 sin θ + cos θ)` is equal to `underlinebb(5/7)`.

Explanation:

sin θ = 2 cos θ 

⇒ `tan θ = (sin θ)/(cos θ)`

= 2 

Equivalently set cos θ = c, sin θ = 2c and substitute:

`(3 sin θ - cos θ)/(3 sin θ + cos θ)` 

= `(3 xx 2c - c)/(3 xx 2c + c)` 

= `(6c - c)/(6c + c)`

= `(5c)/(7c)`

= `5/7`

The sign of c cancels, so the result is `5/7`.