NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.6 Question 8

✅ Step-by-Step Solution

1. Differentiate both coordinates: dx/dt=\(a \left(\frac{\frac{\tan^{2}{\left(\frac{t}{2} \right)}}{2} + \frac{1}{2}}{\tan{\left(\frac{t}{2} \right)}} - \sin{\left(t \right)}\right)\), dy/dt=\(a \cos{\left(t \right)}\).
2. Divide the two rates: dy/dx=(dy/dt)/(dx/dt)=\(\frac{\cos{\left(t \right)}}{\frac{\frac{\tan^{2}{\left(\frac{t}{2} \right)}}{2} + \frac{1}{2}}{\tan{\left(\frac{t}{2} \right)}} - \sin{\left(t \right)}}\).
3. Simplify to \(\tan{\left(t \right)}\). This quotient requires dx/dt≠0; any cancelled zero requires a separate limiting or curve check.