Let $E={\sin }^{-1}\sin 17+{\cos }^{-1}\cos 27+{\tan }^{-1}\tan 37$

Since, ${\sin }^{-1}\sin 17=5\pi -17$, ${\cos }^{-1}\cos 27=27-8\pi$

and ${\tan }^{-1}\tan 37=37-15\pi$

Now, $E=5\mathrm{\pi }-17+27-8\mathrm{\pi }+37-15\mathrm{\pi }$

$\Rightarrow E=47-18\mathrm{\pi }$

Therefore, $k=47, \lambda =18$

Hence, $k+\lambda =18+47=62$