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Question
If 24cosθ = 7 sinθ, find sinθ + cosθ.
Solution
24cosθ = 7sinθ
⇒ `("sin" θ)/("cos"θ) = (24)/(7)`
⇒ tanθ = `(24)/(7) = "Perpendicular"/"Base"`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((24)^2 + (7)^2`
= `sqrt(576 + 49)`
= `sqrt(625)`
= 25
sinθ + cosθ
= `"Perpendicular"/"Hypotenuse" + "Base"/"Hypotenuse"`
= `(24)/(25) + (7)/(25)`
= `(24 + 7)/(25)`
= `(31)/(25)`.
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