without wanting to over explain, new max amplitude = (2 x max amplitude) x (cos (.5 angle in radians))
90 degrees is pi/2 radians, 45 degrees is pi/4 radians so if we take max amplitude as 1, then it becomes
2x(cos (pi/4)) = 1.4
if amplitude was 2 then it becomes 2.8 etc.
My original answer of increase by 1/4 was a bit out, it was only when I actually put the numbers in the formula that I realised by how much.
for a visual demonstration go here and scroll down to phase difference applet