Learn English – Which is correct (if any): “please let me know what do you think”? or “please let me know what you think”

I often come across if otherwise, if not, if opposed, and the like in business communications as a shorthand. I would avoid them if possible.

Otherwise means differently or alternatively, so if otherwise posits an alternative scenario. The trick, of course, is to be mindful of which scenario is being referred to, especially when context is limited. To the original question, if you wanted to use if otherwise to see if the boss agrees with your approach, you would need to write something like

I am planning to do X and Y. I think that is the approach you prefer; please let me know if otherwise.

As originally written, you ask

I am planning to do X and Y; please let me know if I am not planning to do X and Y

which strains logic.

Using otherwise in this way can be quite vague, as there are a number of alternative scenarios which could equally apply:

… if someone else is planning to do X and Y [instead of me]

… if someone else is already doing X and Y [instead of planning]

… if someone else is planning to do A and B [instead of X and Y]

It is better to write explicitly:

I am planning to do X and Y. Please let me know if you prefer a different approach.

As others have noted, it seems a very odd construction. Technically, it's grammatically correct, but the context of that statement seems very limited. For example, I could only imagine saying that to describe of a conditional or hypothetical situation. For example:

"We have a procedure in place for this: You send me a request for information. I write you a letter. I let you know that I have sent you a letter. You get the information once you receive my letter."

Aside from that, it doesn't seem to make sense to me to use "I let you know that I have sent you a letter." Any other intended meaning seems to imply a different tense, to properly frame the context of the statement:

"I'm letting you know that I have sent you a letter." (The focus is on the present act of letting "you" know, occurring at this very moment. As RegDwigнt notes, this might be redundant, since the rest of the sentences is already making the informative statement. That being said, it may be an intentional use of overly-formal language, in which you are "officially" making the announcement.)

"I will let you know that I have sent a letter." (Indicating the future act that will happen, after "I" have sent the letter.)

"I let you know that I [had] sent you a letter." (Indicating the past moment when "I" announced the sending of the letter.)

In short, the original statement's "correctness" is very much related to what you're actually trying to communicate with the statement.