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Question

Find dydx, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

x = sin t, y = cos 2t.

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Solution

Given, x = sin t, y = cos 2t

Differentiating w.r.t. t, we get

dxdt=cos t and dydt=(sin 2t)2 dydx=dydtdxdt=dydt×dydx ( dydx=dy/dtdx/dt)=2sin 2tcos t=2(2sin t cos t)cos t=4 sin t( sin 2θ=2 sin θcosθ)


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