S.T. $\cot \left({\sin }^{-1}\sqrt{\frac{13}{17}}\right)=\sin \left({\mathrm{Tan}}^{-1}2/3\right)$

Let ${\sin }^{-1}\sqrt{\frac{13}{17}}=\alpha \Rightarrow \sin \alpha =\sqrt{\frac{13}{17}}$

$\Rightarrow \cot \alpha =\frac{2}{\sqrt{13}}$

Let  ${\mathrm{Tan}}^{-1}\left(\frac{2}{3}\right)=\beta \Rightarrow \mathrm{Tan}\beta =\frac{2}{3}$

$\Rightarrow \mathrm{Sin}\beta =\frac{2}{\sqrt{13}}$$\therefore$$\cot \alpha =\sin \beta$

$\Rightarrow \cot \left({\sin }^{-1}\sqrt{13/17}\right)=\sin \left({\mathrm{Tan}}^{-1}\frac{2}{3}\right)$