Question

If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to ______.

Options

• `5/14`

• `3/14`

• `1/14`

• 0

Answer 1

If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to `underlinebb(5/14)`.

Explanation:

Given, tan θ = `4/5`

∴ sin θ = `4/sqrt(41)` and cos θ = `5/sqrt(41)`

Now, `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)`

= `(5 xx 4/sqrt(41) - 3 xx 5/sqrt(41))/(4/sqrt(41) + 2 xx 5/sqrt(41))`

= `5/14`