Question

If 5cosθ = 3, find the value of `(4cosθ - sinθ)/(2cosθ + sinθ)`

Answer 1

If 5cosθ = 3

⇒ cosθ = `(3)/(5) = "Base"/"Hypotenuse"`

Perpendicular
= `sqrt(("Hypotenuse")^2 - ("Base")^2`
= `sqrt((5)^2 - (3)^2`
= `sqrt(25 - 9)`
= `sqrt(16)`
= 4

sinθ = `"Perpendicular"/"Hypotenuse" = (4)/(5)`

`(4cosθ - sinθ)/(2cosθ + sinθ)`

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

= `(12/5 - 4/5)/(6/5 + 4/5)`

= `(8/5)/(10/5)`

= `(4)/(5)`.