A level - Equilibrium

I know this question has been asked before, but the answer in that closed thread doesn’t seem right.
In the last question of the M1 equilibrium paper in madasmaths. The question asks specifically to minimize tension. It doesn’t specify whether the string is taught or whether we are trying to minimize both force P and tension. Why can’t force P be applied directly upwards against the weight such that the tension is 0. Doesn’t that minimize tension?
https://madasmaths.com/archive/maths_booklets/mechanics/m1_equilibrium.pdf
Scroll to the last question in the page from the above link

For some reason, the previous reply has disappeared. It may be being moderated for whatever reason.
As a placeholder, youre correct. Tension would be minimised (0) when P is vertical (W). P is minimised at 60 degrees as per the solution and you can derive it by horizontal/vertical/harmonic identity or a simple sketch/justification similar to madas solution. Id guess the question should really say P is minimum, rather than T.

Ya i got a notification for ur reply but couldn’t find it. I guess the solution is more of a minimum of both P and T.