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If x=cost and y=sint , prove that (dy)/(...

If `x=cost` and `y=sint` , prove that `(dy)/(dx)=1/(sqrt(3))` at `t=(2pi)/3`

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We know that
`frac{d y} { d x}=frac{frac{d y }{ d t} }frac{d x}{ d t}={cost} /-sin t`
`frac{d y}{d x}=-cot (t)`
`(frac{d y}{d x})_{x=frac{2 pi}{3}}=-cot (frac{2 pi}{3})`
`(frac{d y}{d x})_{x=frac{2 pi}{3}}=cot (frac{pi}{3})=frac{1}{sqrt{3}}`
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