**Given,**

x = a sin t

**Differentiating both sides with respect to t, we get**

**\(\frac{dx}{dt}=\)** a cos t ..**.(i)**

**Again,**

**∵ y = a [ cos t + log (tan\(\frac{t}{2}\))]**

**Differentiating both sides with respect to t, we get**

**Differentiating both sides with respect to t, we get**

**\(\frac{d^2y}{dx^2}=-cosec^2\,t.\frac{dt}{dx}\)**

⇒ **\(\frac{d^2y}{dx^2}=-cosec^2\,t.\frac{1}{a\,cos\,t}\) **

**\(=\frac{-\,cosec^2\,t}{a\,cos\,t}\)**