Hello,
could anybody give me a hint for 1) and 2) ?
\(\displaystyle \mbox{1) Montrer: }\, \arcsin\left(\dfrac{1}{\sqrt{5\,}}\right)\, =\, \dfrac{1}{2}\, \arctan\left(\dfrac{4}{3}\right)\)
\(\displaystyle \mbox{2) Montrer, pour tout }\, x\, \in\, \mathbb{R}:\, \arcsin(\mbox{th}\, x)\, =\, \arctan(\mbox{sh}\, x)\)
For 1) I have tried using sin^2(X) on the left side and tan^2(X)/1+tan^2(X) on the right side but it didn't work...
could anybody give me a hint for 1) and 2) ?
\(\displaystyle \mbox{1) Montrer: }\, \arcsin\left(\dfrac{1}{\sqrt{5\,}}\right)\, =\, \dfrac{1}{2}\, \arctan\left(\dfrac{4}{3}\right)\)
\(\displaystyle \mbox{2) Montrer, pour tout }\, x\, \in\, \mathbb{R}:\, \arcsin(\mbox{th}\, x)\, =\, \arctan(\mbox{sh}\, x)\)
For 1) I have tried using sin^2(X) on the left side and tan^2(X)/1+tan^2(X) on the right side but it didn't work...
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