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प्रश्न
If cotθ = `(1)/sqrt(3)`, show that `(1 - cos^2θ)/(2 - sin^2θ) = (3)/(5)`
उत्तर
cotθ = `(1)/sqrt(3)`
⇒ cotθ = `(1)/"tanθ" = (1)/sqrt(3) = "Base"/"Perpendicular"`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((sqrt(3))^2 + 1`
= `sqrt(3 + 1)`
= 2
cosθ = `"Base"/"Hypotenuse" = (1)/(2)`,
sinθ = `"Perpendicular"/"Hypotenuse" = sqrt(3)/(2)`
To show: `(1 - cos^2θ)/(2 - sin^2θ) = (3)/(5)`
`(1 - cos^2θ)/(2 - sin^2θ)`
= `(1 - (cosθ)^2)/(2 - (sinθ)^2)`
= `(1 - 1/4)/(2 - 3/4)`
= `(3/4)/(5/4)`
= `(3)/(5)`.
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