Let ey=(1+α+1−α1+α−1−α)e^y=\left(\frac{\sqrt{1+\alpha}+\sqrt{1-\alpha}}{\sqrt{1+\alpha}-\sqrt{1-\alpha}}\right)…

Mathematics

Problem

Let ey=(1+α+1−α1+α−1−α)e^y=\left(\frac{\sqrt{1+\alpha}+\sqrt{1-\alpha}}{\sqrt{1+\alpha}-\sqrt{1-\alpha}}\right) and tan⁡(x2)=1−α1+α\tan\left(\frac{x}{2}\right)=\sqrt{\frac{1-\alpha}{1+\alpha}}, α∈[−1,0)∪(0,1]\alpha\in[-1,0)\cup(0,1] then find dydx∣x=π3\frac{dy}{dx}\bigg|_{x=\frac{\pi}{3}}.

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