Soit \(x\in\R\). On pose \(t=\Arctan(\sh x)\).
1
Établir les relations \[\tan t=\sh x \qquad\qquad \frac{1}{\cos t}=\ch x \qquad\qquad \sin t=\tanh x\]
2
Montrer que \(x = \ln \big(\tan\big(\frac{t}{2}+\frac{\pi}{4}\big)\big)\).
Soit \(x\in\R\). On pose \(t=\Arctan(\sh x)\).
Établir les relations \[\tan t=\sh x \qquad\qquad \frac{1}{\cos t}=\ch x \qquad\qquad \sin t=\tanh x\]
Montrer que \(x = \ln \big(\tan\big(\frac{t}{2}+\frac{\pi}{4}\big)\big)\).