Question

If tanθ = `5/2` then `(4 sinθ + cosθ)/(4sinθ − cosθ)` is equal to ________.

विकल्प

• `11/9`

• `3/2`

• `9/11`

• 4

Answer 1

If tanθ = `5/2` then `(4 sinθ + cosθ)/(4sinθ − cosθ)` is equal to `underlinebb(11/9)`.

Explanation:

tanθ = `5/2`

tanθ = `"opposite"/"adjacent" = 5/2`

∴ h = `sqrt(p^2 + b^2)`

= `sqrt((5)^2 + (2)^2)`

= `sqrt(25 + 4)`

= `sqrt29`

sinθ = `"opposite"/"hypotenuse" = 5/sqrt29`

cosθ = `"adjacent"/"hypotenuse" = 2/sqrt29`

`(4 sin θ + cos θ)/(4 sin θ - cos θ)`

= `(4 xx 5/sqrt29 + 2/sqrt29)/(4 xx 5/sqrt29 - 2/sqrt29)`

= `(20/sqrt29 + 2/sqrt29)/(20/sqrt29 + 2/sqrt29)`

= `((20 + 2)/sqrt29)/((20 - 2)/sqrt29)`

= `(22/sqrt29)/(18/sqrt29)`

= `22/8`

= `11/9`