Really hung up on this inverse trig function problem's solution. Actually I think my difficulty is in the algebra involved (not the actual trig), because; sin(arcsin(x)) = x, so really I'm wondering why (5/13) + pi/4 = 17sqrt2/26. Can anyone explain to me why that is in detail?

if you can't see the image, the problem is:

sin ( arcsin (5/13) + pi/4) = 17 sqrt 2 / 26

WHY?