Question

If 24cosθ = 7 sinθ, find sinθ + cosθ.

Answer 1

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)`.