*NOTE that 1/root2 = cos45*^{o} = sin45^{o}.

*and sin(A+B) = sinAcosB + cosAsinB.*

*So sinx/root2 + cosx/root2 = sinx cos45*^{o} + cosx sin45^{o} = sin(x+45^{o}).

*So sin*^{-1}(sinx+cosx/root2) = sin^{-1}(sin(x+45^{o})) = **x + 45**^{o} (or) **x + pi/4**