If find and

Given:

To find: and

given

Now finding the first derivative of the above equation with respect to t, we get

Now taking out the constant term, we get

Now applying the sum rule of differentiation, we get

Now we know derivative of cosθ=-sinθ, and derivative of so applying the derivation of the above equation, we get

And the derivative of tanθ =sec²θ, so the above equation becomes,

Now substituting we get

Cancelling the like terms, we get

But we know 2 sinθcosθ=sin2θ, we get

But we know sin²θ+cos²θ=1⇒ cos²θ=1-sin²θ, so the above equation becomes

Now also given y=a sin⁡t

Now finding the first derivative of the above equation with respect to t, we get

Now we know derivative of sinθ=cosθ, so applying the derivation of the above equation, we get

Now finding the second derivative of the above equation with respect to t, we get

Now we know derivative of cosθ=-sinθ, so applying the derivation of the above equation, we get

Now we know,

Now substituting values from equation (i) and (ii), we get

Now finding the second derivative of the above equation with respect to x, we get

Now we know derivative of tanθ=sec²θ, so applying the derivation of the above equation, we get

Now substituting value from equation (i), we get

But , so the above equation becomes

Hence and are the required values.