Hi there. This much easier to understand if Icould draw a simple diagram, but I will try and describe things :
Lift L, dragD, Thrust T, Weight W, climb angle theta.
Assume thrust is along flight path.
1.Resolve along flight path results in
T=D+Wsin(theta)---means you need more thrust to climb
2.Resolve normal toflight path results in
L=Wcos(theta)--means you need
slightly less lift in the climb.
Induced drag is a different matter, and for a given lift it increases with lower speed(i.e higher incidence)Hence there is a minimum total drag speed.If you are mathematically inclined Glauert describes it well in his classic book
Keith