The Maharaja would be extremely careful while dealing with the hundredth tiger which was supposed to be the reason for his death. On encountering the hundredth one, he will take a careful aim at the tiger and will shoot it. When it falls in a crumpled heap, he would be filled with joy and will leave the place hastily.
Not that he faced no dangers. There were times when the bullet missed its mark, the tiger leapt upon him and he fought the beast with his bare hands. Each time it was the Maharaja who won. At another time he was in danger of losing his throne. A high-ranking British officer visited Pratibandapuram. He was very fond of hunting tigers. And fonder of being photographed with the tigers he had shot.
(The Tiger King)
Prove that:
\( \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left( \frac{1 - x}{1 + x} \right), \quad x \in [0, 1] \)