If `x=asint` and `y=a(cost+logtant/2)` , find `(d^2y)/(dx^2)` .

Explanation

`x=a sin t and y=a(cos t+log tan frac{t}{2})`

On differentiating with respect to t, we get
`

frac{d x}{d t}=frac{d}{d t}(a sin t)=a cos t`


and


`frac{d y}{d t}=frac{d}{d t}[a(cos t+log tan frac{t}{2})]=a(-sin t+frac{1}{tan frac{t}{2}} times sec ^{2} frac{t}{2} times frac{1}{2}) `
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