Question

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Answer 1

Verified answer

Respuesta:

Opción d.

[tex]AC=m*cos(x)+n*cos(y)[/tex]

Formulas:

ley del seno:  [tex]\frac{A}{sen(a)}=\frac{B}{sen(b)}=\frac{C}{sen(c)}[/tex]

seno de una suma o resta: [tex]sen(\alpha \pm \beta )=sen(\alpha )*cos(\beta ) \pm cos(\alpha )*sen(\beta )[/tex]

Explicación paso a paso:

Por ley del seno:

[tex]\frac{AC}{sen(\pi -(x+y))}=\frac{n}{sen(x)}\\\\AC=\frac{n}{sen(x)}*sen(\pi -(x+y))[/tex]

[tex]sen(\pi-(x+y) )=sen(\pi )*cos(x+y)-cos(\pi )*sen(x+y)\\=0*cos(x+y)-(-1)*sen(x+y)\\=sen(x+y)\\=sen(x)*cos(y)+cos(x)*sen(y)[/tex]

Remplazo:

[tex]AC=\frac{n}{sen(x)} *(sen(x)*cos(y)+cos(x)*sen(y))\\\\AC=\frac{n}{sen(x)}*sen(x)*cos(y)+ \frac{n}{sen(x)}*cos(x)*sen(y)\\\\AC=n *cos(y)+\frac{n}{sen(x)}*cos(x) *sen(y)[/tex]

Por ley del seno:

[tex]\frac{n}{sen(x)}=\frac{m}{sen(y)}[/tex]

Remplazo:

[tex]AC=n*cos(y)+\frac{m}{sen(y)} *cos(x)*sen(y)\\\\AC=n*cos(y)+m*cos(x)[/tex]

Opción d.