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