Mathematics

Problem

Answer the following (internal choice): a. If

\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)

, then prove that

\frac{dy}{dx} = \sqrt{\frac{1-y^2}{1-x^2}}

. b. If

x = a \left( \cos \theta + \log \tan \frac{\theta}{2} \right)

and

y = \sin \theta

, then find

\frac{d^2 y}{dx^2}

\theta = \frac{\pi}{4}