Question

If ${\sin }^{-1}\sin 17+{\cos }^{-1}\cos 27+{\tan }^{-1}\tan 37$ is equal to $k-\lambda \pi$ , then the value of $k+\lambda$ is

Answer 1

Answer: 62

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, $E=5\pi -17+27-8\pi +37-15\pi$
$\Rightarrow E=47-18\pi$
Therefore, $k=47,\lambda =18$
Hence, $k+\lambda =18+47=62$