Trigonométrie Exemples

\frac{1 - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}

$\frac{1 - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}$

Étape 1

Réécrivez

1

$1$ comme

1^{2}

$1^{2}$ .

\frac{1^{2} - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}

$\frac{1^{2} - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}$

Étape 2

Réécrivez

(\cos (x) + \sin (x)) (\cos (x) + \sin (x))

$(\cos (x) + \sin (x)) (\cos (x) + \sin (x))$ comme

{(\cos (x) + \sin (x))}^{2}

${(\cos (x) + \sin (x))}^{2}$ .

\frac{1^{2} - {(\cos (x) + \sin (x))}^{2}}{\sin (x) \cos (x)}

$\frac{1^{2} - {(\cos (x) + \sin (x))}^{2}}{\sin (x) \cos (x)}$

Étape 3

Les deux termes étant des carrés parfaits, factorisez à l’aide de la formule de la différence des carrés,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ où

a = 1

$a = 1$ et

b = \cos (x) + \sin (x)

$b = \cos (x) + \sin (x)$ .

\frac{(1 + \cos (x) + \sin (x)) (1 - (\cos (x) + \sin (x)))}{\sin (x) \cos (x)}

$\frac{(1 + \cos (x) + \sin (x)) (1 - (\cos (x) + \sin (x)))}{\sin (x) \cos (x)}$

Étape 4

Appliquez la propriété distributive.

\frac{(1 + \cos (x) + \sin (x)) (1 - \cos (x) - \sin (x))}{\sin (x) \cos (x)}

$\frac{(1 + \cos (x) + \sin (x)) (1 - \cos (x) - \sin (x))}{\sin (x) \cos (x)}$