3M serie (trigonomètrie) Exercice1 Soit A=1+cos2x+√3 sin2x )=cosx + √3 ...
3M serie (trigonom?trie) Exercice1 Soit A=1+cos2x+3 sin2x 1)Montrer que 2sin(x+/6)=cosx + 3 sinx. 2)En d?duire que A=4cosx sin(x+/6),puis d?duire la valeur de cos(/12). 3)R?soudre dans IR puis dans[-,] :A=0. Exercice2 SoitB= sin 4x
4 sin x
1) Pour quelles valeurs de x B existe. 2) R?soudre dans IR : B=0 3) Montrer que B=cosx cos2x. 4) Montrer que cos(/5). cos(2/5)=1/4
Exercice3 1)Montrer que sin4x+cos4x-1/4 cos4x=3/4 2)Simplifier alors S= cos4x+ cos4(x+/6)+ cos4(x+2/6)+ cos4(x+3/6)+ cos4(x+4/6)+ cos4(x+5/6) Exercice4 R?soudre dans IR puis dans [0,2] 1)2sin2x-(3+1 )sinx+3/2=0. 2)sinx=cosx 3)4cos2x=1 4)sinx + cosx=1 5)(2sinx-1)(2sinx+3)0
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