Question

If 12 cotθ = 13, find the value of `(2sinθ  cosθ)/(cos^2θ - sin^2θ)`.

Answer 1

cot θ = `(13)/(12)`

⇒ `cosθ /sinθ  = (13)/(12)`

⇒ `"Base"/"Hypotenuse" xx "Hypotenuse"/"Perpendicular" = (13)/(12)`

⇒ `"Base"/"Perpendicular" = (13)/(12)`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((12)^2 + (13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`

`(2sinθ  cosθ)/(cos^2θ - sin^2θ)`

= `(2 xx 12/sqrt(313) xx 13/sqrt(313))/((13/sqrt(313))^2 - (12/sqrt(313))^2`

= `(312/313)/(169/313 - 144/313)`

= `(312/313)/(25/313)`

= `(312)/(25)`.