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प्रश्न
Find `(dy)/(dx)` if x = a cosec θ, y = b cot θ at θ = `π/4`
उत्तर
x = a cosec θ, y = b cot θ
Consider, y = b cot θ
Differentiating w.r.t. θ
`(dy)/(dθ) = b(-cosec^2θ)`
= `-b cosec^2θ`
Consider, x = a cosec θ
Differentiating w.r.to θ
`(dy)/(dθ)` = a(-cosec θ. cot θ)
= -a cosec θ. cot θ
Now `(dy)/(dx)` = `((dy)/(dθ))/((dy)/(dθ))``
= `(-b cosec^2θ)/(-a cosec θ . cot θ)`
= `b/a (cosecθ)/(cotθ)`
`(dy/dx)_(at θ = π/4) = b/a (cosec (π/4))/cot (π/4)`
= `b/a (sqrt2/1)`
= `sqrt2 b/a`
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