Bonjour ! ;)
Réponse :
- Rappel n°1 : cot (x) = [tex]\frac{1}{tan(x)}[/tex] = [tex]\frac{cos(x)}{sin(x)}[/tex]
- Rappel n°2 : tan (x) = [tex]\frac{sin(x)}{cos(x)}[/tex]
cot (x) [ 1 + tan (x) ] - 1
= cot (x) * 1 + cot (x) * tan (x) - 1
= [tex]\frac{cos(x)}{sin(x)}[/tex] + [tex]\frac{cos(x)}{sin(x)}[/tex] * [tex]\frac{sin(x)}{cos(x)}[/tex] - 1
= [tex]\frac{cos(x)}{sin(x)}[/tex] + 1 - 1
= [tex]\frac{cos(x)}{sin(x)}[/tex]
On a donc bien : cot (x) [ 1 + tan (x) ] - 1 = [tex]\frac{cos(x)}{sin(x)}[/tex] !
