Question

Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ

Answer 1

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`