# Are you ready for JEE-5

Geometry Level 5

$\large\tan^{-1} x+\cos^{-1}\left(\dfrac{y}{\sqrt{1+y^2}}\right)=\sin^{-1} \dfrac{3}{\sqrt{10}}$

$$(x,y)\in\mathbb{Z^+}$$

The above equation has $$\color{blue}{\zeta}$$ ordered $$(x,y)$$ solutions and let:

$\large\left(x_i+y_i\right)_{\text{least}}\times \left(y_i-x_i\right)_{\text{max}}=\color{blue}{\beta}$

where $$(x_i,y_i)$$ denote the $$ith$$ ordered solution in the solution set of above equation.

$\Large \color{blue}{\zeta}+\color{blue}{\beta}=\ ?$

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