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Question
Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ
Solution
a cot θ, y = b cosec θ
Differentiating x and y w.r.t. x, we get
`"dx"/"dθ" = a"d"/"dθ"(cotθ)`
= a (– cosec2θ)
= – cosec2θ
and
`"dy"/"dθ" = b"d"/"dθ"("cosec" "θ")`
= b (– cosec θ cot θ)
= – b cosec θ cot θ
∴ `"dy"/"dx" = (("dy"/"dθ"))/(("dx"/"dθ"))`
= `(-b "cosec" "θ"cotθ)/(-a "cosec"^2θ)`
= `b/a.cotθ/("cosec" "θ")`
= `b/a xx cosθ/sinθ xx sinθ`
= `(b/a)cosθ`
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