Formula for Construction of a Pi-Chart.

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Let $(x, y)$ be such that $\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2}$

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Prove that $\tan \left[\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right]+\tan \left[\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right]=\frac{2 b}{a}$

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The set of values of a for which the point (a-1, a+1) lies outside the circle x2 + y2 = 8 and inside the circle $x^{2}+y^{2}-12 x+12 y-62=0$ is

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Formula for Construction of a Pi-Chart.

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