Question

help me to find out this solution ♡♡​

Answer 1

Answer:

4(1+t)/(1-t)

Step-by-step explanation:

$x = log( \sqrt{1 - {t}^{2} } ) \: \: and \: \: y = \frac{1 + t}{1 - t}$

Differentiating both functions with respect to t, we get,

$\frac{dx}{dt} = \frac{ - t}{1 - {t}^{2} } \: \: and \: \: \frac{dy}{dt} = \frac{2}{(1 - t)^{2} }$

Now, we will divide 2nd equation by 1st one to obtain dy/dx

$\frac{dy}{dx} = \frac{ \frac{2}{(1 - t)^{2} } }{ \frac{ - t}{1 - {t}^{2} } }$

$\frac{dy}{dx} = \frac{ - 2}{(1 - t)^{2} } \frac{(1 - t^{2}) }{t}$

$\frac{dy}{dx} = - \frac{2(1 + t)}{t(1 - t)}$