Mathematics - Continuity - Differentiability Question with Solution | TestHub

Let $f:(0,\pi )\to \mathbf{R}$ be a function given by $f(x)=$ $\{\begin{array}{cc}{\left(\frac{8}{7}\right)}^{\frac{\tan 8x}{\tan 7x}},& 0<x<\frac{\pi }{2}\\ \mathrm{a}-8,& x=\frac{\pi }{2}\\ (1+|\cot x|{)}^{\frac{\mathrm{b}}{}|\tan x|},& \frac{\pi }{2}<x<\pi \end{array}$
where $\mathrm{a},\mathrm{b}\in \mathbf{Z}$. If $f$ is continuous at $x=\frac{\pi }{2}$, then ${\mathrm{a}}^2+{\mathrm{b}}^2$ is equal to