Versed sine vs. versed cosine

The versed sine = 2*sin(x/2)^2 = 1-cos(x)
and coversed sine = 2*sin(pi/4-x/2)^2 = 1-sin(x)

doesn't it follow that
the versed cosine = 2*cos(x/2)^2 = 1+cos(x)
and coversed cosine = 2*cos(pi/4-x/2)^2 = 1+sin(x)?

In the trig books I've seen, "versed cosine" = "versed sine"
and "1+cos(x)" isn't defined. Does "1+cos(x)" have a
different name?

TIA
.