If $y =\large \frac{2}{\sqrt {a^2-b^2}}$$\tan^{-1} \bigg( \sqrt {\large\frac{a+b}{a-b}}\tan\frac{x}{2} \bigg)$. Prove that $\large \frac{dy}{dx}=\frac{1}{a-b\cos x} .$

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