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प्रश्न
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (θ – sin θ), y = a (1 + cos θ)
उत्तर
Here c = a (θ - sinθ)
y = a (1 + cosθ)
Differentiating (1) & (2) w.r.t.t t, we get
`dx/(dθ) = a [1 - cos θ]`
`dy/(dθ) = a [-sin θ]`
= -a sin θ
`dy/dx = (dy/(dθ))/(dx/(dθ)) = (-1 sin θ)/ (a (1 - cos θ))`
= `(- sin θ)/ (1- cos θ) = (-2 sin θ //2 cos θ//2)/(2 sin^2 θ//2)`
= `-cot θ/2`
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