# 1 exercice 6 1 résoudre dans r léquation arccoscos

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Exercice 6 1. Résoudre dans R l’équation Arccoscos x = x 0 . 2. Même question avec Arccoscos x = x . Exercice 7 – Simplifier les expressions. a ) f ( x )=Arcsin parenleftBigg x +1 radicalbig 2( x 2 +1) parenrightBigg b ) f ( x )=2Arctan radicalbigg 1+ x 1 x c ) f ( x )=Arcsin radicalbigg 1+sin x 2 x 2 d ) f ( x )=Arccos radicalbigg 1+sin x 2 Arcsin radicalbigg 1+cos x 2 . Exercice 8 – Résoudre l’équation 2Arcsin( x )=Arcsin ( 2 x 1 x 2 ) (on pourra faire un changement de variables). Exercice 9 1. Exprimer tan( a + b + c ) en fonction de tan( a ) , tan( b ) et tan( c ) . 2. En exploitant la formule précédente, calculer Arctan2+Arctan3+Arctan(2+ 3) . Exercice 10 – Soit f la fonction définie sur R \ { 1 } par f ( x )=Arctan parenleftBig 1+ x 1 x parenrightBig . 1. Exprimer la dérivée de f . 2. En déduire une expression simplifiée de f ( x ) en fonction de Arctan x . Exercice 11 – Résoudre l’équation Arctan x +Arctan( x 3)= 7 π 12 . Exercice 12 – Résoudre les équations suivantes, d’inconnue x dans R : 1. Arcsin( x )=Arcsin 4 5 +Arcsin 5 13 .
• Fall '19
• Mathématiques, Lycée Louis-le-Grand

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