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