Question 178
Show that, for all $x, y, z, w$,
$$
(x - w)(y - z) + (y - w)(z - x) + (z - w)(x - y) = 0,
$$
and
$$
\sin(x - w)\sin(y - z) + \sin(y - w)\sin(z - x) + \sin(z - w)\sin(x - y) = 0.
$$
$$
(x - w)(y - z) + (y - w)(z - x) + (z - w)(x - y) = 0,
$$
and
$$
\sin(x - w)\sin(y - z) + \sin(y - w)\sin(z - x) + \sin(z - w)\sin(x - y) = 0.
$$