Question

la demonstracnion de seno (x+y+z)

Answer 1

Se sabe que sen(a+b) = sen(a)cos(b) + sen(b)cos(a) y que:

cos(a+b) = cos(a)cos(b) - sen(a)sen(b)

hacemos x + y = a

sen(a + z) = sen(a) cos(z) + sen(z) cos(a)

Luego sen(x+y+z) = sen(x+y)cos(z) + sen(z) cos(x+y)

Reemplazando:

sen(x+y+z) = [sen(x)cos(y) + sen(y)cos(x)] cos(z) +

+ sen(z) [cos(x)cos(y) - sen(x)sen(y)] =

= sen(x)cos(y)cos(z) + sen(y)cos(x)cos(z) + sen(z)cos(x)cos(y) -

- sen(z)sen(x)sen(y)

Saludos Herminio