Question

Calcula sen(135°-x-y)

Answer 1

Respuesta:

$Sen(135-x - y)=\dfrac{4+\sqrt{2}}{6}$

Explicación:

Primero calculamos la hipotenusa del triángulo de la imagen :

$h^{2}=1^{2}+ (2\sqrt{2} )^{2}$

$h^{2}=1+ 8$

h = 3

Ahora calculamos la expresión pedida :

$Sen(135-x - y)=Sen(135-(x + y))$

$Sen(135-x - y)=Sen135Cos(x + y)-Cos135Sen(x+y)$

Reduciendo al primer cuadrante :

$Sen(135-x - y)=Sen45Cos(x + y)-(-Cos45)Sen(x+y)$

Reemplazando :

$Sen(135-x - y)=(\dfrac{1}{\sqrt{2}})(\dfrac{2\sqrt{2} }{3})+(\dfrac{1}{\sqrt{2}})(\dfrac{1}{3} )$

$Sen(135-x - y)=\dfrac{2}{3}+\dfrac{\sqrt{2}}{6}$

$Sen(135-x - y)=\dfrac{4+\sqrt{2}}{6}$