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

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