1) sin inverse (4/5) +sin inverse (5/13) +sin inverse (6/25)=90

As sin^-1x + sin^-1y = ${\sin }^{-1}(x\sqrt{1-y^2}+y\sqrt{1-x^2})$
So sin^-1(4/5) + sin^-1(5/13) = sin^-1(63/65)
And again using the above formula we have 
sin^-1(63/65) + sin^-1 (6/25) = sin^-1(0.99997)  or sin^-1(1)
And sin^-1(1) = 90
Hence proved.