If x = a (cos t + t sin t) and y = a (sin t – t cos t), find d2y/dx2.

Q17 of 147 Page 191

If x = a (cos t + t sin t) and y = a (sin t – t cos t), find d²y/dx².

Given, x = a (cos t + t sin t) and y = (sin t – t cos t)

To find we need to find out and

So, and

x = a (cos t + t sin t)

Differentiating with respect to t.

⇒

y = a (sin t – t cos t)

Differentiating with respect to t.

⇒

∴

Differentiating dy/dx with respect to t

And

⇒

∴

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