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Question
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = a(cos t + log tan t/2), y = a sin t`
Solution
x = a `(cos t + log tan t/2) y = a sin t`
`dx/dt = a [- sin t + 1/tan(t/2) d/dt tan t/2]`
`= a [- sin t + 1/sin t] & dy/dt = a cos t`
`= dy/dt= dy/dt div dx/dt`
`= (a cos t)/(a (cos^2 t)/(sin t))`
= tan t
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