If x and y are connected parametrically by the equations given, without eliminating the parameter, Find `(dy)/(dx)`.
`x=a(cost+logtan((t)/(2))), y=asint`

Explanation

The given equations are `x=a(cos t+log(tan( t/2))),y=a sin t`

Then,
`dx/dt=a[ d/dt (cost)+ d/dt(log(tan (t/2)) )]

=a[−sint+ 1/tan(t/2). d/dt(tan (t/2))]`

`=a[−sint+cot(t/2).sec ^2(t/2) .d/dt( t/2)]`

`=a[−sint+ cos(t/2)/sin(t/2)times 1/cos ^2(t/2)times1/2 ]`

`=a[−sint+ 1/(2sin(t/2)cos(t/2))]`

`=a( (-sin^2t+1)/sint)`

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