I dont understand how to use CAST diagrams with reciprocal trigonometric ratios

I was looking at the edexcel year 2 pure textbooks and they are doing CAST diagrams differently??

What are you saying is different? Perhaps it would be been more "usual" in cast to say
cos(210) = cos(150)
or
cos(210) = - cos(-30)
but both reduce to
cos(210) = -cos(30).
But its fairly clear the triangles (30-60-90) in the two quadrants (1 and 3) are equivalent apart from the sign change on the x-axis, so cos() flips sign between 30 and 210.

how comes this inverse rule isnt applicable to sec 60?

There is nothing special about sec/cosec/cot, cast applies to them just by interpreting them as cos/sin/tan.
sec(60) = 1/cos(60) = ...
it does work, though thats a fairly trivial example as its in quadrant 1.

how comes its not inversed to be cos 30 (just like you did with the other one)

For the first one
sec(210) = 1/cos(210) = ...
so do cast on cos(210) then take the reciprocal to get back to sec(210).

For the second
sec(60) = 1/cos(60) = ...
so its simply the reciprocal of cos(60) as there is no need to use cast to reason about the sign.

Its the same in both cases.

For the first one
sec(210) = 1/cos(210) = ...
so do cast on cos(210) then take the reciprocal to get back to sec(210).

For the second
sec(60) = 1/cos(60) = ...
so its simply the reciprocal of cos(60) as there is no need to use cast to reason about the sign.

Its the same in both cases.

-cos(pi/3) = -1/2
if thats where you mean? You could simply evalate on your calcuator if unsure.

Ohhhhhh i didn't know I had to use my calculator