Prove that sensitivity of a galvanometer is maximum when the deflection is 90 degree. Please prove it mathematically.

Galvanometer is an ammeter which can be used from both sides as an ammeter if not connected properly would make the needle go in reverse direction and break it hence the galvanometer was made with deflection angle as 180 this was twice as an ammeter it ensured that the needle won`t break if even connected in wrong way the needle is in the centre hence it can go 90 in both directionshence the max deflection is 90