Struggling with mate in 2 moves (Yusupov)

From Build up Your Chess (1)  - first book in the first set of 3 books to take a player up to 1500, part of Yusupov's 9-series training course.

I'm finding Chapter 9, mate in 2 moves, to be incredibly, hair-tearingly difficult. Here are two examples. Any tips?

White to move and mate in 2. There is exactly 1 correct solution in each problem.

First one is

C8

rxc8

Rd7

I do think this is one of the hardest tactical chapters in the book, somehow.

Wait nvm dunno lol

Yeah that doesn't work because of Kxc6

Yeah, black has Kxc6.

They're deceptive, aren't they?

I believe the first is 1. Rd7 Kxc6 2. Cxb8=N or 1...Kxa7 2. c8=N

I think it's a case of seeing what doesn't work and finding a move that fixes that problem.

Yes, that is the correct and only answer. I looked at that for half an hour and couldn't get it.

I'm on 6 points with 3 to go, so at least it's a pass. I can feel it improving my visualisations, brain-training and so on, but it's also giving me a headache.

It's a very difficult book in my opinion, even the first one.

What is the point of puzzles like this? In both cases white is easily winning, in a real game you won't search for mate in 2 moves in such positions.

Visualisation, working efficiently through a broad range of moves.

It's a theme in Quality Chess (Aagaard et al) who believe in hard work being the road to improvement, without chess salespersons who write books like 'Become a Grandmaster in 3 Easy Steps'.

I'm passing the lessons but mostly getting 'passes' and a few 'goods' - far off top marks. I hope it filters through to my slow games. I need to stop playing blitz too. It's like being fed a nutritious and healthy chess breakfast to then pig out on cream eclairs for the day.

I found I did really well in the tactics but some of the strategy ones e.g. Outposts were really hard.

Yes, correct!

Generally, each book has one of its 24 lessons devoted to mate in x. About 5 examples then 12 test positions.

Also Kxd6 Qb8#

Here's one final one. It's instructive.

There are multiple other responses to Rb6+

I can take with the rook.

In a real game I'd play 1.cxb8=Q+,Kxc6 2.Qb5+,Kc7 3.Qd7# because I'd quickly find that it wins by force and black has no stalemate nonsense.

It's a bad problem because the mate in 2 isn't essential.  For mate in two it's 1.Rd7,Nxc6 2.cxb8=Q# or 1...Kxc6 2.cxb8=N# to both attack the king and defend the rook. The rook and bishops wall off the king's potential escape squares so using board vision we can greatly reduce our choice of candidates.  The rook the king can take meanwhile is excess material so there's no need to hold onto it.  The threat against the Rd7 looks problematic at first until you realize a knight defends it after promotion.