I can think of a few valid reasons for moderator intervention regarding accepted answer:

1. One user accepts another user's junk answers as a way of gaming the reputation system
2. The answer owner requests deletion, having realized that the answer is totally wrong and being unable to get it unaccepted by the question owner (discussed in http://meta.math.stackexchange.com/q/9827)
3. The accepted answer is correctly flagged as spam or offensive speech.

In the hypothetical example

user has asked a question regarding how is the function $\sin x$ can be approximated by polynomials, and the accepted answer states that $\sin x=\cos(\pi+x)$.

I can't rule out the possibility that the question owner found this answer the most helpful out of those given. If they already knew how to approximate $\cos x$, this answer does solve the problem. (This is not as far-fetched as one might think. I recently saw a question along the lines of "what should I add to sine wave to get $0$", where the answer was to add $-\sin x$, and this turned out to be what the OP was looking for.)

The accepted status of an answer does not prevent it from being downvoted into graying out and being commented upon, with critical comments raising to prominence through comment votes. I think this is quite enough.

To give a worse (still hypothetical) example: if someone asks

How to prove that the standard Cantor set has measure zero?

and accepts the answer

Since the real line is countable, so is the Cantor set, and countable sets have measure zero.

I would not want this to be an item on moderator's plate. Let the users deal with it. The accepted status of such an answer gives useful information about the question owner.

I can think of a few valid reasons for moderator intervention regarding accepted answer:

1. One user accepts another user's junk answers as a way of gaming the reputation system
2. The answer owner requests deletion, having realized that the answer is totally wrong and being unable to get it unaccepted by the question owner (discussed in http://meta.math.stackexchange.com/q/9827)
3. The accepted answer is correctly flagged as spam or offensive speech.

In the hypothetical example

user has asked a question regarding how is the function $\sin x$ can be approximated by polynomials, and the accepted answer states that $\sin x=\cos(\pi+x)$.

I can't rule out the possibility that the question owner found this answer the most helpful out of those given. If they already knew how to approximate $\cos x$, this answer does solve the problem. (This is not as far-fetched as one might think. I recently saw a question along the lines of "what should I add to sine wave to get $0$", where the answer was to add $-\sin x$, and this turned out to be what the OP was looking for.)

The accepted status of an answer does not prevent it from being downvoted into graying out and being commented upon, with critical comments raising to prominence through comment votes. I think this is quite enough.

To give a worse (still hypothetical) example: if someone asks

How to prove that the standard Cantor set has measure zero?

and accepts the answer

Since the real line is countable, so is the Cantor set, and countable sets have measure zero.

I would not want this to be an item on moderator's plate. Let the users deal with it. The accepted status of such an answer gives useful information about the question owner.