From pythagorean theorem: A 2+B 2 = C 2,

From the different expressions of area: ab=ch,

∴c/(ab)= 1/h，

∴ 1/a^2+ 1/b^2

=(a^2+b^2)/(ab)^2

=(c/ab)^2

=( 1/h)^2

= 1/h^2.