Let $a$ and $b$ be two real numbers. If $a > 0$ and $a ^ { 2 } - b ^ { 2 } = 1$ show that there exists a unique $\theta \in \mathbb { R }$ such that $a = \operatorname { ch } \theta$ and $b = \operatorname { sh } \theta$.
Let $a$ and $b$ be two real numbers. If $a > 0$ and $a ^ { 2 } - b ^ { 2 } = 1$ show that there exists a unique $\theta \in \mathbb { R }$ such that $a = \operatorname { ch } \theta$ and $b = \operatorname { sh } \theta$.